diff --git a/Credits.rst b/Credits.rst index 0f76292c..e52b4872 100644 --- a/Credits.rst +++ b/Credits.rst @@ -105,8 +105,13 @@ Tobias Dwyer * Added examples for the shape classes. Jen Bradley + * Bug fixes for ``gsd_shape_spec`` to correctly comply with GSD specifications. * Fixed error where ``__repr__`` would fail for polyhedra with multiple face types. +* Increased accuracy of stored data for PlatonicFamily solids +* Added shape families for Archimedean, Catalan, and Johnson solids. +* Added shape family for prisms and antiprisms. +* Added shape family for equilateral pyramids and dipyramids. Source code ----------- diff --git a/coxeter/families/__init__.py b/coxeter/families/__init__.py index efbb9ac2..6895c2aa 100644 --- a/coxeter/families/__init__.py +++ b/coxeter/families/__init__.py @@ -17,7 +17,15 @@ reproducing the exact set of shapes from publications. """ -from .common import PlatonicFamily, RegularNGonFamily +from .common import ( + ArchimedeanFamily, + CatalanFamily, + JohnsonFamily, + PlatonicFamily, + PrismAntiprismFamily, + PyramidDipyramidFamily, + RegularNGonFamily, +) from .doi_data_repositories import _doi_shape_collection_factory, _KeyedDefaultDict from .plane_shape_families import ( Family323Plus, @@ -53,6 +61,11 @@ "Family423", "Family523", "PlatonicFamily", + "ArchimedeanFamily", + "CatalanFamily", + "JohnsonFamily", + "PrismAntiprismFamily", + "PyramidDipyramidFamily", "RegularNGonFamily", "ShapeFamily", "TabulatedShapeFamily", diff --git a/coxeter/families/common.py b/coxeter/families/common.py index 67a983a2..bb86624c 100644 --- a/coxeter/families/common.py +++ b/coxeter/families/common.py @@ -83,3 +83,74 @@ def make_vertices(cls, n): "Icosahedron", "Octahedron", and "Tetrahedron". """, ) + +ArchimedeanFamily = TabulatedGSDShapeFamily.from_json_file( + os.path.join(_DATA_FOLDER, "archimedean.json"), + classname="ArchimedeanFamily", + docstring="""The family of Archimedean solids (13 total). +The following parameters are required by this class: + - name: The name of the ArchimedeanFamily solid. Options are "Cuboctahedron", \ + "Icosidodecahedron", "Truncated Tetrahedron", "Truncated Octahedron", \ + "Truncated Cube", "Truncated Icosahedron", "Truncated Dodecahedron", \ + "Rhombicuboctahedron", "Rhombicosidodecahedron", "Truncated \ + Cuboctahedron", "Truncated Icosidodecahedron", "Snub Cuboctahedron", \ + and "Snub Icosidodecahedron". +""", +) + +CatalanFamily = TabulatedGSDShapeFamily.from_json_file( + os.path.join(_DATA_FOLDER, "catalan.json"), + classname="CatalanFamily", + docstring="""The family of Catalan solids, also known as Archimedean duals + (13 total). +The following parameters are required by this class: + - name: The name of the CatalanFamily solid. Options are "Deltoidal \ + Hexecontahedron", "DeltoidalIcositetrahedron", "Disdyakis \ + Dodecahedron", "Disdyakis Triacontahedron", "Pentagonal \ + Hexecontahedron", "Pentagonal Icositetrahedron", "Pentakis \ + Dodecahedron", "Rhombic Dodecahedron", "Rhombic \ + Triacontahedron", "Triakis Octahedron", "Tetrakis \ + Hexahedron", "Triakis Icosahedron", and "Triakis Tetrahedron". +""", +) + +JohnsonFamily = TabulatedGSDShapeFamily.from_json_file( + os.path.join(_DATA_FOLDER, "johnson.json"), + classname="JohnsonFamily", + docstring="""The family of Johnson solids (92 total). +The following parameters are required by this class: + - name: The name of the JohnsonFamily solid. A full list is available in \ + 10.1126/science.1220869: :cite:`Damasceno2012`. In general, shape names \ + should have the first character of each word capitalized, with spaces \ + between words (e.g. "Elongated Triangular Cupola"). Pyramids and \ + dipyramids are named from their base polygon (e.g. "Square Pyramid" \ + or "Elongated Pentagonal Dipyramid"). +""", +) + + +PyramidDipyramidFamily = TabulatedGSDShapeFamily.from_json_file( + os.path.join(_DATA_FOLDER, "pyramid_dipyramid.json"), + classname="PyramidDipyramidFamily", + docstring="""The family of regular equilateral pyramids and dipyramids (6 total). +The following parameters are required by this class: + - name: The name of the pyramid or dipyramid. Options are "Triangular Pyramid", \ + "Square Pyramid", "Pentagonal Pyramid", "Triangular Dipyramid", \ + "Square Dipyramid", and "Pentagonal Dipyramid". +""", +) + +PrismAntiprismFamily = TabulatedGSDShapeFamily.from_json_file( + os.path.join(_DATA_FOLDER, "prism_antiprism.json"), + classname="PrismAntiprismFamily", + docstring="""The family of n-gonal prisms and antiprisms with n∈[3,10] (16 total). +The following parameters are required by this class: + - name: The name of the prism or antiprism. Options for prisms are \ + "Triangular Prism", "Square Prism", "Pentagonal Prism", "Hexagonal Prism", \ + "Heptagonal Prism", "Octagonal Prism", "Nonagonal Prism", and \ + "Decagonal Prism". Options for antiprisms are "Triangular Antiprism", \ + "Square Antiprism", "Pentagonal Antiprism", "Hexagonal Antiprism", \ + "Heptagonal Antiprism", "Octagonal Antiprism","Nonagonal Antiprism", \ + and "Decagonal Antiprism". +""", +) diff --git a/coxeter/families/data/archimedean.json b/coxeter/families/data/archimedean.json new file mode 100644 index 00000000..19b4d98e --- /dev/null +++ b/coxeter/families/data/archimedean.json @@ -0,0 +1,2883 @@ +{ + "Cuboctahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.7514130803550182, + 0.0, + 0.0 + ], + [ + -0.3757065401775091, + -0.3757065401775091, + -0.5313292845913055 + ], + [ + -0.3757065401775091, + -0.3757065401775091, + 0.5313292845913055 + ], + [ + -0.3757065401775091, + 0.3757065401775091, + -0.5313292845913055 + ], + [ + -0.3757065401775091, + 0.3757065401775091, + 0.5313292845913055 + ], + [ + 0.0, + -0.7514130803550182, + 0.0 + ], + [ + 0.0, + 0.7514130803550182, + 0.0 + ], + [ + 0.3757065401775091, + -0.3757065401775091, + -0.5313292845913055 + ], + [ + 0.3757065401775091, + -0.3757065401775091, + 0.5313292845913055 + ], + [ + 0.3757065401775091, + 0.3757065401775091, + -0.5313292845913055 + ], + [ + 0.3757065401775091, + 0.3757065401775091, + 0.5313292845913055 + ], + [ + 0.7514130803550182, + 0.0, + 0.0 + ] + ], + "symmetry_group": "[4,3]", + "short_code": "A01" + }, + "Truncated Icosidodecahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.1691014932254225, + -0.2213567284062581, + -0.579519438606063 + ], + [ + -0.1691014932254225, + -0.2213567284062581, + 0.579519438606063 + ], + [ + -0.1691014932254225, + 0.2213567284062581, + -0.579519438606063 + ], + [ + -0.1691014932254225, + 0.2213567284062581, + 0.579519438606063 + ], + [ + -0.08455074661271125, + -0.08455074661271125, + -0.6317746737868987 + ], + [ + -0.08455074661271125, + -0.08455074661271125, + 0.6317746737868987 + ], + [ + -0.08455074661271125, + 0.08455074661271125, + -0.6317746737868987 + ], + [ + -0.08455074661271125, + 0.08455074661271125, + 0.6317746737868987 + ], + [ + -0.08455074661271125, + -0.6317746737868987, + -0.08455074661271125 + ], + [ + -0.08455074661271125, + -0.6317746737868987, + 0.08455074661271125 + ], + [ + -0.08455074661271125, + -0.35816271019980495, + -0.5272642034252275 + ], + [ + -0.08455074661271125, + -0.35816271019980495, + 0.5272642034252275 + ], + [ + -0.08455074661271125, + 0.6317746737868987, + -0.08455074661271125 + ], + [ + -0.08455074661271125, + 0.6317746737868987, + 0.08455074661271125 + ], + [ + -0.08455074661271125, + 0.35816271019980495, + -0.5272642034252275 + ], + [ + -0.08455074661271125, + 0.35816271019980495, + 0.5272642034252275 + ], + [ + 0.08455074661271125, + -0.08455074661271125, + -0.6317746737868987 + ], + [ + 0.08455074661271125, + -0.08455074661271125, + 0.6317746737868987 + ], + [ + 0.08455074661271125, + 0.08455074661271125, + -0.6317746737868987 + ], + [ + 0.08455074661271125, + 0.08455074661271125, + 0.6317746737868987 + ], + [ + 0.08455074661271125, + -0.6317746737868987, + -0.08455074661271125 + ], + [ + 0.08455074661271125, + -0.6317746737868987, + 0.08455074661271125 + ], + [ + 0.08455074661271125, + -0.35816271019980495, + -0.5272642034252275 + ], + [ + 0.08455074661271125, + -0.35816271019980495, + 0.5272642034252275 + ], + [ + 0.08455074661271125, + 0.6317746737868987, + -0.08455074661271125 + ], + [ + 0.08455074661271125, + 0.6317746737868987, + 0.08455074661271125 + ], + [ + 0.08455074661271125, + 0.35816271019980495, + -0.5272642034252275 + ], + [ + 0.08455074661271125, + 0.35816271019980495, + 0.5272642034252275 + ], + [ + 0.1691014932254225, + -0.2213567284062581, + -0.579519438606063 + ], + [ + 0.1691014932254225, + -0.2213567284062581, + 0.579519438606063 + ], + [ + 0.1691014932254225, + 0.2213567284062581, + -0.579519438606063 + ], + [ + 0.1691014932254225, + 0.2213567284062581, + 0.579519438606063 + ], + [ + -0.579519438606063, + -0.1691014932254225, + -0.2213567284062581 + ], + [ + -0.579519438606063, + -0.1691014932254225, + 0.2213567284062581 + ], + [ + -0.579519438606063, + 0.1691014932254225, + -0.2213567284062581 + ], + [ + -0.579519438606063, + 0.1691014932254225, + 0.2213567284062581 + ], + [ + -0.4949686919933518, + -0.30590747501896937, + -0.2736119635870937 + ], + [ + -0.4949686919933518, + -0.30590747501896937, + 0.2736119635870937 + ], + [ + -0.4949686919933518, + 0.30590747501896937, + -0.2736119635870937 + ], + [ + -0.4949686919933518, + 0.30590747501896937, + 0.2736119635870937 + ], + [ + -0.30590747501896937, + -0.2736119635870937, + -0.4949686919933518 + ], + [ + -0.30590747501896937, + -0.2736119635870937, + 0.4949686919933518 + ], + [ + -0.30590747501896937, + 0.2736119635870937, + -0.4949686919933518 + ], + [ + -0.30590747501896937, + 0.2736119635870937, + 0.4949686919933518 + ], + [ + -0.2213567284062581, + -0.579519438606063, + -0.1691014932254225 + ], + [ + -0.2213567284062581, + -0.579519438606063, + 0.1691014932254225 + ], + [ + -0.2213567284062581, + -0.4104179453806406, + -0.4427134568125162 + ], + [ + -0.2213567284062581, + -0.4104179453806406, + 0.4427134568125162 + ], + [ + -0.2213567284062581, + 0.4104179453806406, + -0.4427134568125162 + ], + [ + -0.2213567284062581, + 0.4104179453806406, + 0.4427134568125162 + ], + [ + -0.2213567284062581, + 0.579519438606063, + -0.1691014932254225 + ], + [ + -0.2213567284062581, + 0.579519438606063, + 0.1691014932254225 + ], + [ + -0.4427134568125162, + -0.2213567284062581, + -0.4104179453806406 + ], + [ + -0.4427134568125162, + -0.2213567284062581, + 0.4104179453806406 + ], + [ + -0.4427134568125162, + 0.2213567284062581, + -0.4104179453806406 + ], + [ + -0.4427134568125162, + 0.2213567284062581, + 0.4104179453806406 + ], + [ + -0.6317746737868987, + -0.08455074661271125, + -0.08455074661271125 + ], + [ + -0.6317746737868987, + -0.08455074661271125, + 0.08455074661271125 + ], + [ + -0.6317746737868987, + 0.08455074661271125, + -0.08455074661271125 + ], + [ + -0.6317746737868987, + 0.08455074661271125, + 0.08455074661271125 + ], + [ + -0.2736119635870937, + -0.4949686919933518, + -0.30590747501896937 + ], + [ + -0.2736119635870937, + -0.4949686919933518, + 0.30590747501896937 + ], + [ + -0.2736119635870937, + 0.4949686919933518, + -0.30590747501896937 + ], + [ + -0.2736119635870937, + 0.4949686919933518, + 0.30590747501896937 + ], + [ + -0.5272642034252275, + -0.08455074661271125, + -0.35816271019980495 + ], + [ + -0.5272642034252275, + -0.08455074661271125, + 0.35816271019980495 + ], + [ + -0.5272642034252275, + 0.08455074661271125, + -0.35816271019980495 + ], + [ + -0.5272642034252275, + 0.08455074661271125, + 0.35816271019980495 + ], + [ + -0.35816271019980495, + -0.5272642034252275, + -0.08455074661271125 + ], + [ + -0.35816271019980495, + -0.5272642034252275, + 0.08455074661271125 + ], + [ + -0.35816271019980495, + 0.5272642034252275, + -0.08455074661271125 + ], + [ + -0.35816271019980495, + 0.5272642034252275, + 0.08455074661271125 + ], + [ + -0.4104179453806406, + -0.4427134568125162, + -0.2213567284062581 + ], + [ + -0.4104179453806406, + -0.4427134568125162, + 0.2213567284062581 + ], + [ + -0.4104179453806406, + 0.4427134568125162, + -0.2213567284062581 + ], + [ + -0.4104179453806406, + 0.4427134568125162, + 0.2213567284062581 + ], + [ + 0.2736119635870937, + -0.4949686919933518, + -0.30590747501896937 + ], + [ + 0.2736119635870937, + -0.4949686919933518, + 0.30590747501896937 + ], + [ + 0.2736119635870937, + 0.4949686919933518, + -0.30590747501896937 + ], + [ + 0.2736119635870937, + 0.4949686919933518, + 0.30590747501896937 + ], + [ + 0.4104179453806406, + -0.4427134568125162, + -0.2213567284062581 + ], + [ + 0.4104179453806406, + -0.4427134568125162, + 0.2213567284062581 + ], + [ + 0.4104179453806406, + 0.4427134568125162, + -0.2213567284062581 + ], + [ + 0.4104179453806406, + 0.4427134568125162, + 0.2213567284062581 + ], + [ + 0.6317746737868987, + -0.08455074661271125, + -0.08455074661271125 + ], + [ + 0.6317746737868987, + -0.08455074661271125, + 0.08455074661271125 + ], + [ + 0.6317746737868987, + 0.08455074661271125, + -0.08455074661271125 + ], + [ + 0.6317746737868987, + 0.08455074661271125, + 0.08455074661271125 + ], + [ + 0.35816271019980495, + -0.5272642034252275, + -0.08455074661271125 + ], + [ + 0.35816271019980495, + -0.5272642034252275, + 0.08455074661271125 + ], + [ + 0.35816271019980495, + 0.5272642034252275, + -0.08455074661271125 + ], + [ + 0.35816271019980495, + 0.5272642034252275, + 0.08455074661271125 + ], + [ + 0.2213567284062581, + -0.579519438606063, + -0.1691014932254225 + ], + [ + 0.2213567284062581, + -0.579519438606063, + 0.1691014932254225 + ], + [ + 0.2213567284062581, + -0.4104179453806406, + -0.4427134568125162 + ], + [ + 0.2213567284062581, + -0.4104179453806406, + 0.4427134568125162 + ], + [ + 0.2213567284062581, + 0.4104179453806406, + -0.4427134568125162 + ], + [ + 0.2213567284062581, + 0.4104179453806406, + 0.4427134568125162 + ], + [ + 0.2213567284062581, + 0.579519438606063, + -0.1691014932254225 + ], + [ + 0.2213567284062581, + 0.579519438606063, + 0.1691014932254225 + ], + [ + 0.4427134568125162, + -0.2213567284062581, + -0.4104179453806406 + ], + [ + 0.4427134568125162, + -0.2213567284062581, + 0.4104179453806406 + ], + [ + 0.4427134568125162, + 0.2213567284062581, + -0.4104179453806406 + ], + [ + 0.4427134568125162, + 0.2213567284062581, + 0.4104179453806406 + ], + [ + 0.5272642034252275, + -0.08455074661271125, + -0.35816271019980495 + ], + [ + 0.5272642034252275, + -0.08455074661271125, + 0.35816271019980495 + ], + [ + 0.5272642034252275, + 0.08455074661271125, + -0.35816271019980495 + ], + [ + 0.5272642034252275, + 0.08455074661271125, + 0.35816271019980495 + ], + [ + 0.30590747501896937, + -0.2736119635870937, + -0.4949686919933518 + ], + [ + 0.30590747501896937, + -0.2736119635870937, + 0.4949686919933518 + ], + [ + 0.30590747501896937, + 0.2736119635870937, + -0.4949686919933518 + ], + [ + 0.30590747501896937, + 0.2736119635870937, + 0.4949686919933518 + ], + [ + 0.4949686919933518, + -0.30590747501896937, + -0.2736119635870937 + ], + [ + 0.4949686919933518, + -0.30590747501896937, + 0.2736119635870937 + ], + [ + 0.4949686919933518, + 0.30590747501896937, + -0.2736119635870937 + ], + [ + 0.4949686919933518, + 0.30590747501896937, + 0.2736119635870937 + ], + [ + 0.579519438606063, + -0.1691014932254225, + -0.2213567284062581 + ], + [ + 0.579519438606063, + -0.1691014932254225, + 0.2213567284062581 + ], + [ + 0.579519438606063, + 0.1691014932254225, + -0.2213567284062581 + ], + [ + 0.579519438606063, + 0.1691014932254225, + 0.2213567284062581 + ] + ], + "symmetry_group": "[5,3]", + "short_code": "A11" + }, + "Truncated Cuboctahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.14407260500220836, + 0.3478220369627532, + -0.5515714689232981 + ], + [ + -0.14407260500220836, + 0.3478220369627532, + 0.5515714689232981 + ], + [ + -0.14407260500220836, + -0.34782203696275316, + -0.5515714689232981 + ], + [ + -0.14407260500220836, + -0.34782203696275316, + 0.5515714689232981 + ], + [ + -0.14407260500220836, + -0.5515714689232981, + 0.3478220369627532 + ], + [ + -0.14407260500220836, + -0.5515714689232981, + -0.34782203696275316 + ], + [ + -0.14407260500220836, + 0.5515714689232981, + 0.3478220369627532 + ], + [ + -0.14407260500220836, + 0.5515714689232981, + -0.34782203696275316 + ], + [ + 0.14407260500220836, + 0.3478220369627532, + -0.5515714689232981 + ], + [ + 0.14407260500220836, + 0.3478220369627532, + 0.5515714689232981 + ], + [ + 0.14407260500220836, + -0.34782203696275316, + -0.5515714689232981 + ], + [ + 0.14407260500220836, + -0.34782203696275316, + 0.5515714689232981 + ], + [ + 0.14407260500220836, + -0.5515714689232981, + 0.3478220369627532 + ], + [ + 0.14407260500220836, + -0.5515714689232981, + -0.34782203696275316 + ], + [ + 0.14407260500220836, + 0.5515714689232981, + 0.3478220369627532 + ], + [ + 0.14407260500220836, + 0.5515714689232981, + -0.34782203696275316 + ], + [ + 0.3478220369627532, + -0.14407260500220836, + -0.5515714689232981 + ], + [ + 0.3478220369627532, + -0.14407260500220836, + 0.5515714689232981 + ], + [ + 0.3478220369627532, + 0.14407260500220836, + -0.5515714689232981 + ], + [ + 0.3478220369627532, + 0.14407260500220836, + 0.5515714689232981 + ], + [ + 0.3478220369627532, + -0.5515714689232981, + -0.14407260500220836 + ], + [ + 0.3478220369627532, + -0.5515714689232981, + 0.14407260500220836 + ], + [ + 0.3478220369627532, + 0.5515714689232981, + -0.14407260500220836 + ], + [ + 0.3478220369627532, + 0.5515714689232981, + 0.14407260500220836 + ], + [ + -0.34782203696275316, + -0.14407260500220836, + -0.5515714689232981 + ], + [ + -0.34782203696275316, + -0.14407260500220836, + 0.5515714689232981 + ], + [ + -0.34782203696275316, + 0.14407260500220836, + -0.5515714689232981 + ], + [ + -0.34782203696275316, + 0.14407260500220836, + 0.5515714689232981 + ], + [ + -0.34782203696275316, + -0.5515714689232981, + -0.14407260500220836 + ], + [ + -0.34782203696275316, + -0.5515714689232981, + 0.14407260500220836 + ], + [ + -0.34782203696275316, + 0.5515714689232981, + -0.14407260500220836 + ], + [ + -0.34782203696275316, + 0.5515714689232981, + 0.14407260500220836 + ], + [ + -0.5515714689232981, + -0.14407260500220836, + 0.3478220369627532 + ], + [ + -0.5515714689232981, + -0.14407260500220836, + -0.34782203696275316 + ], + [ + -0.5515714689232981, + 0.14407260500220836, + 0.3478220369627532 + ], + [ + -0.5515714689232981, + 0.14407260500220836, + -0.34782203696275316 + ], + [ + -0.5515714689232981, + 0.3478220369627532, + -0.14407260500220836 + ], + [ + -0.5515714689232981, + 0.3478220369627532, + 0.14407260500220836 + ], + [ + -0.5515714689232981, + -0.34782203696275316, + -0.14407260500220836 + ], + [ + -0.5515714689232981, + -0.34782203696275316, + 0.14407260500220836 + ], + [ + 0.5515714689232981, + -0.14407260500220836, + 0.3478220369627532 + ], + [ + 0.5515714689232981, + -0.14407260500220836, + -0.34782203696275316 + ], + [ + 0.5515714689232981, + 0.14407260500220836, + 0.3478220369627532 + ], + [ + 0.5515714689232981, + 0.14407260500220836, + -0.34782203696275316 + ], + [ + 0.5515714689232981, + 0.3478220369627532, + -0.14407260500220836 + ], + [ + 0.5515714689232981, + 0.3478220369627532, + 0.14407260500220836 + ], + [ + 0.5515714689232981, + -0.34782203696275316, + -0.14407260500220836 + ], + [ + 0.5515714689232981, + -0.34782203696275316, + 0.14407260500220836 + ] + ], + "symmetry_group": "[4,3]", + "short_code": "A10" + }, + "Icosidodecahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.6739935637720124, + 0.0 + ], + [ + 0.0, + 0.6739935637720124, + 0.0 + ], + [ + 0.1094968920018681, + -0.3369967818860062, + -0.5733331698467344 + ], + [ + 0.1094968920018681, + 0.3369967818860062, + -0.5733331698467344 + ], + [ + 0.1771696929214991, + -0.5452722471908928, + 0.35433938584299823 + ], + [ + 0.1771696929214991, + 0.5452722471908928, + 0.35433938584299823 + ], + [ + 0.2866665849233672, + -0.2082754653048867, + 0.5733331698467344 + ], + [ + 0.2866665849233672, + 0.2082754653048867, + 0.5733331698467344 + ], + [ + 0.4638362778448663, + -0.3369967818860062, + -0.35433938584299823 + ], + [ + 0.4638362778448663, + 0.3369967818860062, + -0.35433938584299823 + ], + [ + -0.5733331698467344, + 0.0, + -0.35433938584299823 + ], + [ + -0.2866665849233672, + -0.2082754653048867, + -0.5733331698467344 + ], + [ + -0.2866665849233672, + 0.2082754653048867, + -0.5733331698467344 + ], + [ + 0.5733331698467344, + 0.0, + 0.35433938584299823 + ], + [ + 0.3961634769252353, + -0.5452722471908928, + 0.0 + ], + [ + 0.3961634769252353, + 0.5452722471908928, + 0.0 + ], + [ + 0.35433938584299823, + 0.0, + -0.5733331698467344 + ], + [ + -0.3961634769252353, + -0.5452722471908928, + 0.0 + ], + [ + -0.3961634769252353, + 0.5452722471908928, + 0.0 + ], + [ + -0.6410059707663655, + -0.2082754653048867, + 0.0 + ], + [ + -0.6410059707663655, + 0.2082754653048867, + 0.0 + ], + [ + 0.6410059707663655, + -0.2082754653048867, + 0.0 + ], + [ + 0.6410059707663655, + 0.2082754653048867, + 0.0 + ], + [ + -0.35433938584299823, + 0.0, + 0.5733331698467344 + ], + [ + -0.4638362778448663, + -0.3369967818860062, + 0.35433938584299823 + ], + [ + -0.4638362778448663, + 0.3369967818860062, + 0.35433938584299823 + ], + [ + -0.17716969292149912, + -0.5452722471908928, + -0.35433938584299823 + ], + [ + -0.17716969292149912, + 0.5452722471908928, + -0.35433938584299823 + ], + [ + -0.1094968920018681, + -0.3369967818860062, + 0.5733331698467344 + ], + [ + -0.1094968920018681, + 0.3369967818860062, + 0.5733331698467344 + ] + ], + "symmetry_group": "[5,3]", + "short_code": "A02" + }, + "Rhombicosidodecahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.1442842451438814, + -0.1442842451438814, + -0.6111978705117256 + ], + [ + -0.1442842451438814, + -0.1442842451438814, + 0.6111978705117256 + ], + [ + -0.1442842451438814, + 0.1442842451438814, + -0.6111978705117256 + ], + [ + -0.1442842451438814, + 0.1442842451438814, + 0.6111978705117256 + ], + [ + -0.1442842451438814, + -0.6111978705117256, + -0.1442842451438814 + ], + [ + -0.1442842451438814, + -0.6111978705117256, + 0.1442842451438814 + ], + [ + -0.1442842451438814, + 0.6111978705117256, + -0.1442842451438814 + ], + [ + -0.1442842451438814, + 0.6111978705117256, + 0.1442842451438814 + ], + [ + 0.0, + -0.3777410578278036, + -0.5220253029716849 + ], + [ + 0.0, + -0.3777410578278036, + 0.5220253029716849 + ], + [ + 0.0, + 0.3777410578278035, + -0.5220253029716849 + ], + [ + 0.0, + 0.3777410578278035, + 0.5220253029716849 + ], + [ + 0.1442842451438814, + -0.1442842451438814, + -0.6111978705117256 + ], + [ + 0.1442842451438814, + -0.1442842451438814, + 0.6111978705117256 + ], + [ + 0.1442842451438814, + 0.1442842451438814, + -0.6111978705117256 + ], + [ + 0.1442842451438814, + 0.1442842451438814, + 0.6111978705117256 + ], + [ + 0.1442842451438814, + -0.6111978705117256, + -0.1442842451438814 + ], + [ + 0.1442842451438814, + -0.6111978705117256, + 0.1442842451438814 + ], + [ + 0.1442842451438814, + 0.6111978705117256, + -0.1442842451438814 + ], + [ + 0.1442842451438814, + 0.6111978705117256, + 0.1442842451438814 + ], + [ + -0.5220253029716849, + 0.0, + -0.3777410578278036 + ], + [ + -0.5220253029716849, + 0.0, + 0.3777410578278035 + ], + [ + -0.2334568126839221, + -0.4669136253678442, + -0.3777410578278036 + ], + [ + -0.2334568126839221, + -0.4669136253678442, + 0.3777410578278035 + ], + [ + -0.2334568126839221, + 0.4669136253678442, + -0.3777410578278036 + ], + [ + -0.2334568126839221, + 0.4669136253678442, + 0.3777410578278035 + ], + [ + -0.4669136253678442, + -0.3777410578278036, + -0.2334568126839221 + ], + [ + -0.4669136253678442, + -0.3777410578278036, + 0.2334568126839221 + ], + [ + -0.4669136253678442, + 0.3777410578278035, + -0.2334568126839221 + ], + [ + -0.4669136253678442, + 0.3777410578278035, + 0.2334568126839221 + ], + [ + -0.6111978705117256, + -0.1442842451438814, + -0.1442842451438814 + ], + [ + -0.6111978705117256, + -0.1442842451438814, + 0.1442842451438814 + ], + [ + -0.6111978705117256, + 0.1442842451438814, + -0.1442842451438814 + ], + [ + -0.6111978705117256, + 0.1442842451438814, + 0.1442842451438814 + ], + [ + -0.3777410578278036, + -0.5220253029716849, + 0.0 + ], + [ + -0.3777410578278036, + -0.2334568126839221, + -0.4669136253678442 + ], + [ + -0.3777410578278036, + -0.2334568126839221, + 0.4669136253678442 + ], + [ + -0.3777410578278036, + 0.2334568126839221, + -0.4669136253678442 + ], + [ + -0.3777410578278036, + 0.2334568126839221, + 0.4669136253678442 + ], + [ + -0.3777410578278036, + 0.5220253029716849, + 0.0 + ], + [ + 0.2334568126839221, + -0.4669136253678442, + -0.3777410578278036 + ], + [ + 0.2334568126839221, + -0.4669136253678442, + 0.3777410578278035 + ], + [ + 0.2334568126839221, + 0.4669136253678442, + -0.3777410578278036 + ], + [ + 0.2334568126839221, + 0.4669136253678442, + 0.3777410578278035 + ], + [ + 0.4669136253678442, + -0.3777410578278036, + -0.2334568126839221 + ], + [ + 0.4669136253678442, + -0.3777410578278036, + 0.2334568126839221 + ], + [ + 0.4669136253678442, + 0.3777410578278035, + -0.2334568126839221 + ], + [ + 0.4669136253678442, + 0.3777410578278035, + 0.2334568126839221 + ], + [ + 0.6111978705117256, + -0.1442842451438814, + -0.1442842451438814 + ], + [ + 0.6111978705117256, + -0.1442842451438814, + 0.1442842451438814 + ], + [ + 0.6111978705117256, + 0.1442842451438814, + -0.1442842451438814 + ], + [ + 0.6111978705117256, + 0.1442842451438814, + 0.1442842451438814 + ], + [ + 0.3777410578278035, + -0.5220253029716849, + 0.0 + ], + [ + 0.3777410578278035, + -0.2334568126839221, + -0.4669136253678442 + ], + [ + 0.3777410578278035, + -0.2334568126839221, + 0.4669136253678442 + ], + [ + 0.3777410578278035, + 0.2334568126839221, + -0.4669136253678442 + ], + [ + 0.3777410578278035, + 0.2334568126839221, + 0.4669136253678442 + ], + [ + 0.3777410578278035, + 0.5220253029716849, + 0.0 + ], + [ + 0.5220253029716849, + 0.0, + -0.3777410578278036 + ], + [ + 0.5220253029716849, + 0.0, + 0.3777410578278035 + ] + ], + "symmetry_group": "[5,3]", + "short_code": "A09" + }, + "Rhombicuboctahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.2429760130015836, + -0.2429760130015836, + -0.5865959859197646 + ], + [ + -0.2429760130015836, + -0.2429760130015836, + 0.5865959859197646 + ], + [ + -0.2429760130015836, + 0.2429760130015836, + -0.5865959859197646 + ], + [ + -0.2429760130015836, + 0.2429760130015836, + 0.5865959859197646 + ], + [ + -0.2429760130015836, + -0.5865959859197646, + -0.2429760130015836 + ], + [ + -0.2429760130015836, + -0.5865959859197646, + 0.2429760130015836 + ], + [ + -0.2429760130015836, + 0.5865959859197646, + -0.2429760130015836 + ], + [ + -0.2429760130015836, + 0.5865959859197646, + 0.2429760130015836 + ], + [ + 0.2429760130015836, + -0.2429760130015836, + -0.5865959859197646 + ], + [ + 0.2429760130015836, + -0.2429760130015836, + 0.5865959859197646 + ], + [ + 0.2429760130015836, + 0.2429760130015836, + -0.5865959859197646 + ], + [ + 0.2429760130015836, + 0.2429760130015836, + 0.5865959859197646 + ], + [ + 0.2429760130015836, + -0.5865959859197646, + -0.2429760130015836 + ], + [ + 0.2429760130015836, + -0.5865959859197646, + 0.2429760130015836 + ], + [ + 0.2429760130015836, + 0.5865959859197646, + -0.2429760130015836 + ], + [ + 0.2429760130015836, + 0.5865959859197646, + 0.2429760130015836 + ], + [ + -0.5865959859197646, + -0.2429760130015836, + -0.2429760130015836 + ], + [ + -0.5865959859197646, + -0.2429760130015836, + 0.2429760130015836 + ], + [ + -0.5865959859197646, + 0.2429760130015836, + -0.2429760130015836 + ], + [ + -0.5865959859197646, + 0.2429760130015836, + 0.2429760130015836 + ], + [ + 0.5865959859197646, + -0.2429760130015836, + -0.2429760130015836 + ], + [ + 0.5865959859197646, + -0.2429760130015836, + 0.2429760130015836 + ], + [ + 0.5865959859197646, + 0.2429760130015836, + -0.2429760130015836 + ], + [ + 0.5865959859197646, + 0.2429760130015836, + 0.2429760130015836 + ] + ], + "symmetry_group": "[4,3]", + "short_code": "A08" + }, + "Snub Cuboctahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.5739621787969352, + -0.1696619243454313, + -0.3120569303126987 + ], + [ + -0.5739621787969352, + 0.16966192434543123, + 0.3120569303126987 + ], + [ + -0.5739621787969352, + -0.3120569303126987, + 0.16966192434543123 + ], + [ + -0.5739621787969352, + 0.3120569303126987, + -0.1696619243454313 + ], + [ + 0.5739621787969351, + -0.1696619243454313, + 0.3120569303126987 + ], + [ + 0.5739621787969351, + 0.16966192434543123, + -0.3120569303126987 + ], + [ + 0.5739621787969351, + -0.3120569303126987, + -0.1696619243454313 + ], + [ + 0.5739621787969351, + 0.3120569303126987, + 0.16966192434543123 + ], + [ + -0.1696619243454313, + -0.5739621787969352, + 0.3120569303126987 + ], + [ + -0.1696619243454313, + 0.5739621787969351, + -0.3120569303126987 + ], + [ + -0.1696619243454313, + -0.3120569303126987, + -0.5739621787969352 + ], + [ + -0.1696619243454313, + 0.3120569303126987, + 0.5739621787969351 + ], + [ + 0.16966192434543123, + -0.5739621787969352, + -0.3120569303126987 + ], + [ + 0.16966192434543123, + 0.5739621787969351, + 0.3120569303126987 + ], + [ + 0.16966192434543123, + -0.3120569303126987, + 0.5739621787969351 + ], + [ + 0.16966192434543123, + 0.3120569303126987, + -0.5739621787969352 + ], + [ + -0.3120569303126987, + -0.5739621787969352, + -0.1696619243454313 + ], + [ + -0.3120569303126987, + 0.5739621787969351, + 0.16966192434543123 + ], + [ + -0.3120569303126987, + -0.1696619243454313, + 0.5739621787969351 + ], + [ + -0.3120569303126987, + 0.16966192434543123, + -0.5739621787969352 + ], + [ + 0.3120569303126987, + -0.5739621787969352, + 0.16966192434543123 + ], + [ + 0.3120569303126987, + 0.5739621787969351, + -0.1696619243454313 + ], + [ + 0.3120569303126987, + -0.1696619243454313, + -0.5739621787969352 + ], + [ + 0.3120569303126987, + 0.16966192434543123, + 0.5739621787969351 + ] + ], + "symmetry_group": "[4,3]+", + "short_code": "A12" + }, + "Snub Icosidodecahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.6118893397049292, + -0.1919129421845664, + 0.05234613580478883 + ], + [ + 0.6118893397049292, + -0.1919129421845664, + -0.05234613580478883 + ], + [ + -0.49097280996575354, + 0.1919129421845664, + 0.36890972046363835 + ], + [ + 0.49097280996575354, + 0.1919129421845664, + -0.36890972046363835 + ], + [ + -0.6245850047588037, + 0.09876376904350899, + 0.1188215010464438 + ], + [ + 0.6245850047588037, + 0.09876376904350899, + -0.1188215010464438 + ], + [ + -0.39782443534457973, + 0.49152459642219404, + -0.1188215010464438 + ], + [ + 0.39782443534457973, + 0.49152459642219404, + 0.1188215010464438 + ], + [ + -0.5447525101535341, + -0.09876376904350899, + 0.3278256853297322 + ], + [ + 0.5447525101535341, + -0.09876376904350899, + -0.3278256853297322 + ], + [ + -0.18684432211158913, + 0.5211513970900553, + -0.3278256853297322 + ], + [ + 0.18684432211158913, + 0.5211513970900553, + 0.3278256853297322 + ], + [ + -0.31701954067850335, + 0.43395524139707176, + 0.35378060807252343 + ], + [ + 0.31701954067850335, + 0.43395524139707176, + -0.35378060807252343 + ], + [ + -0.5766482452409576, + 0.25295230831049964, + -0.13217863041005842 + ], + [ + 0.5766482452409576, + 0.25295230831049964, + 0.13217863041005842 + ], + [ + -0.341689138214878, + -0.25295230831049964, + 0.4829522977505422 + ], + [ + 0.341689138214878, + -0.25295230831049964, + -0.4829522977505422 + ], + [ + -0.47214615309931335, + -0.43395524139707176, + -0.05234613580478883 + ], + [ + 0.47214615309931335, + -0.43395524139707176, + 0.05234613580478883 + ], + [ + -0.3155859762955116, + 0.11186596471092447, + -0.5494276629921971 + ], + [ + 0.3155859762955116, + 0.11186596471092447, + 0.5494276629921971 + ], + [ + -0.13106121008066438, + -0.11186596471092447, + -0.6199098519201406 + ], + [ + 0.13106121008066438, + -0.11186596471092447, + 0.6199098519201406 + ], + [ + -0.46630321242937894, + -0.37291587527113845, + 0.23973803078561953 + ], + [ + 0.46630321242937894, + -0.37291587527113845, + -0.23973803078561953 + ], + [ + -0.5561062276740045, + -0.21737249019456453, + -0.23973803078561953 + ], + [ + 0.5561062276740045, + -0.21737249019456453, + 0.23973803078561953 + ], + [ + -0.5073872475632851, + 0.37291587527113845, + 0.13217863041005842 + ], + [ + 0.5073872475632851, + 0.37291587527113845, + -0.13217863041005842 + ], + [ + -0.2173064928160209, + -0.49152459642219404, + 0.35378060807252343 + ], + [ + 0.2173064928160209, + -0.49152459642219404, + -0.35378060807252343 + ], + [ + -0.07928492173602802, + -0.5211513970900553, + -0.36890972046363835 + ], + [ + 0.07928492173602802, + -0.5211513970900553, + 0.36890972046363835 + ], + [ + -0.22676056941422396, + -0.590288365465703, + -0.1188215010464438 + ], + [ + 0.22676056941422396, + -0.590288365465703, + 0.1188215010464438 + ], + [ + -0.35790818804194496, + -0.4223876280465464, + -0.3278256853297322 + ], + [ + 0.35790818804194496, + -0.4223876280465464, + 0.3278256853297322 + ], + [ + -0.5343260334945243, + 0.05756935502512229, + -0.35378060807252343 + ], + [ + 0.5343260334945243, + 0.05756935502512229, + 0.35378060807252343 + ], + [ + -0.3899076940502452, + -0.16943531973604675, + -0.4829522977505422 + ], + [ + 0.3899076940502452, + -0.16943531973604675, + 0.4829522977505422 + ], + [ + -0.2546717554062699, + 0.21737249019456453, + 0.5494276629921971 + ], + [ + 0.2546717554062699, + 0.21737249019456453, + -0.5494276629921971 + ], + [ + -0.4116878882297255, + 0.329238454905489, + -0.36890972046363835 + ], + [ + 0.4116878882297255, + 0.329238454905489, + 0.36890972046363835 + ], + [ + -0.03134816221818193, + 0.16943531973604675, + -0.6199098519201406 + ], + [ + 0.03134816221818193, + 0.16943531973604675, + 0.6199098519201406 + ], + [ + -0.13974318660561588, + 0.6258681835816381, + -0.05234613580478883 + ], + [ + 0.13974318660561588, + 0.6258681835816381, + 0.05234613580478883 + ], + [ + -0.08980301524462561, + 0.590288365465703, + 0.23973803078561953 + ], + [ + 0.08980301524462561, + 0.590288365465703, + -0.23973803078561953 + ], + [ + -0.04821855583536728, + 0.4223876280465464, + 0.4829522977505422 + ], + [ + 0.04821855583536728, + 0.4223876280465464, + -0.4829522977505422 + ], + [ + -0.16240937229884633, + -0.05756935502512229, + 0.6199098519201406 + ], + [ + 0.16240937229884633, + -0.05756935502512229, + -0.6199098519201406 + ], + [ + -0.06926099767767252, + -0.6258681835816381, + 0.13217863041005842 + ], + [ + 0.06926099767767252, + -0.6258681835816381, + -0.13217863041005842 + ], + [ + -0.06091422088924169, + -0.329238454905489, + 0.5494276629921971 + ], + [ + 0.06091422088924169, + -0.329238454905489, + -0.5494276629921971 + ] + ], + "symmetry_group": "[5,3]+", + "short_code": "A13" + }, + "Truncated Cube": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.20947263010697756, + 0.5057116645502279, + 0.5057116645502279 + ], + [ + -0.20947263010697756, + 0.5057116645502279, + -0.5057116645502279 + ], + [ + -0.20947263010697756, + -0.5057116645502279, + 0.5057116645502279 + ], + [ + -0.20947263010697756, + -0.5057116645502279, + -0.5057116645502279 + ], + [ + 0.20947263010697756, + 0.5057116645502279, + 0.5057116645502279 + ], + [ + 0.20947263010697756, + 0.5057116645502279, + -0.5057116645502279 + ], + [ + 0.20947263010697756, + -0.5057116645502279, + 0.5057116645502279 + ], + [ + 0.20947263010697756, + -0.5057116645502279, + -0.5057116645502279 + ], + [ + 0.5057116645502279, + -0.20947263010697756, + 0.5057116645502279 + ], + [ + 0.5057116645502279, + -0.20947263010697756, + -0.5057116645502279 + ], + [ + 0.5057116645502279, + 0.20947263010697756, + 0.5057116645502279 + ], + [ + 0.5057116645502279, + 0.20947263010697756, + -0.5057116645502279 + ], + [ + 0.5057116645502279, + 0.5057116645502279, + -0.20947263010697756 + ], + [ + 0.5057116645502279, + 0.5057116645502279, + 0.20947263010697756 + ], + [ + 0.5057116645502279, + -0.5057116645502279, + -0.20947263010697756 + ], + [ + 0.5057116645502279, + -0.5057116645502279, + 0.20947263010697756 + ], + [ + -0.5057116645502279, + -0.20947263010697756, + 0.5057116645502279 + ], + [ + -0.5057116645502279, + -0.20947263010697756, + -0.5057116645502279 + ], + [ + -0.5057116645502279, + 0.20947263010697756, + 0.5057116645502279 + ], + [ + -0.5057116645502279, + 0.20947263010697756, + -0.5057116645502279 + ], + [ + -0.5057116645502279, + 0.5057116645502279, + -0.20947263010697756 + ], + [ + -0.5057116645502279, + 0.5057116645502279, + 0.20947263010697756 + ], + [ + -0.5057116645502279, + -0.5057116645502279, + -0.20947263010697756 + ], + [ + -0.5057116645502279, + -0.5057116645502279, + 0.20947263010697756 + ] + ], + "symmetry_group": "[4,3]", + "short_code": "A05" + }, + "Truncated Dodecahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.3679429286191086, + 0.56620594701554 + ], + [ + 0.0, + -0.3679429286191086, + -0.56620594701554 + ], + [ + 0.0, + 0.3679429286191086, + 0.56620594701554 + ], + [ + 0.0, + 0.3679429286191086, + -0.56620594701554 + ], + [ + 0.09671952252964747, + -0.6656150108320557, + 0.059775952298983345 + ], + [ + 0.09671952252964747, + 0.6656150108320557, + 0.059775952298983345 + ], + [ + 0.15649547482863083, + -0.48164354652250135, + 0.4466540424175732 + ], + [ + 0.15649547482863083, + 0.48164354652250135, + 0.4466540424175732 + ], + [ + -0.6259818993145233, + 0.0, + -0.25321499735827824 + ], + [ + -0.4694864244858925, + -0.48164354652250135, + 0.059775952298983345 + ], + [ + -0.4694864244858925, + 0.48164354652250135, + 0.059775952298983345 + ], + [ + -0.31299094965726165, + -0.5953441644258941, + -0.059775952298983345 + ], + [ + -0.31299094965726165, + 0.5953441644258941, + -0.059775952298983345 + ], + [ + -0.15649547482863083, + -0.48164354652250135, + -0.4466540424175732 + ], + [ + -0.15649547482863083, + 0.48164354652250135, + -0.4466540424175732 + ], + [ + 0.31299094965726165, + -0.5953441644258941, + 0.059775952298983345 + ], + [ + 0.31299094965726165, + 0.5953441644258941, + 0.059775952298983345 + ], + [ + 0.6259818993145233, + 0.0, + 0.25321499735827824 + ], + [ + 0.4097104721869091, + -0.29767208221294705, + -0.4466540424175732 + ], + [ + 0.4097104721869091, + 0.29767208221294705, + -0.4466540424175732 + ], + [ + 0.4694864244858925, + -0.48164354652250135, + -0.059775952298983345 + ], + [ + 0.4694864244858925, + 0.48164354652250135, + -0.059775952298983345 + ], + [ + 0.5064299947165565, + 0.0, + 0.4466540424175732 + ], + [ + 0.5064299947165565, + -0.3679429286191086, + -0.25321499735827824 + ], + [ + 0.5064299947165565, + 0.3679429286191086, + -0.25321499735827824 + ], + [ + -0.603149517246204, + -0.29767208221294705, + 0.059775952298983345 + ], + [ + -0.603149517246204, + 0.29767208221294705, + 0.059775952298983345 + ], + [ + 0.603149517246204, + -0.29767208221294705, + -0.059775952298983345 + ], + [ + 0.603149517246204, + 0.29767208221294705, + -0.059775952298983345 + ], + [ + 0.6629254695451873, + -0.11370061790339275, + 0.059775952298983345 + ], + [ + 0.6629254695451873, + 0.11370061790339275, + 0.059775952298983345 + ], + [ + -0.6629254695451873, + -0.11370061790339275, + -0.059775952298983345 + ], + [ + -0.6629254695451873, + 0.11370061790339275, + -0.059775952298983345 + ], + [ + 0.21627142712761416, + -0.29767208221294705, + 0.56620594701554 + ], + [ + 0.21627142712761416, + -0.29767208221294705, + -0.56620594701554 + ], + [ + 0.21627142712761416, + 0.29767208221294705, + 0.56620594701554 + ], + [ + 0.21627142712761416, + 0.29767208221294705, + -0.56620594701554 + ], + [ + 0.19343904505929496, + -0.5953441644258941, + 0.25321499735827824 + ], + [ + 0.19343904505929496, + 0.5953441644258941, + 0.25321499735827824 + ], + [ + -0.21627142712761416, + -0.29767208221294705, + 0.56620594701554 + ], + [ + -0.21627142712761416, + -0.29767208221294705, + -0.56620594701554 + ], + [ + -0.21627142712761416, + 0.29767208221294705, + 0.56620594701554 + ], + [ + -0.21627142712761416, + 0.29767208221294705, + -0.56620594701554 + ], + [ + -0.3499345198879258, + -0.11370061790339275, + 0.56620594701554 + ], + [ + -0.3499345198879258, + -0.11370061790339275, + -0.56620594701554 + ], + [ + -0.3499345198879258, + 0.11370061790339275, + 0.56620594701554 + ], + [ + -0.3499345198879258, + 0.11370061790339275, + -0.56620594701554 + ], + [ + 0.3499345198879258, + -0.11370061790339275, + 0.56620594701554 + ], + [ + 0.3499345198879258, + -0.11370061790339275, + -0.56620594701554 + ], + [ + 0.3499345198879258, + 0.11370061790339275, + 0.56620594701554 + ], + [ + 0.3499345198879258, + 0.11370061790339275, + -0.56620594701554 + ], + [ + -0.5064299947165565, + 0.0, + -0.4466540424175732 + ], + [ + -0.5064299947165565, + -0.3679429286191086, + 0.25321499735827824 + ], + [ + -0.5064299947165565, + 0.3679429286191086, + 0.25321499735827824 + ], + [ + -0.19343904505929496, + -0.5953441644258941, + -0.25321499735827824 + ], + [ + -0.19343904505929496, + 0.5953441644258941, + -0.25321499735827824 + ], + [ + -0.4097104721869091, + -0.29767208221294705, + 0.4466540424175732 + ], + [ + -0.4097104721869091, + 0.29767208221294705, + 0.4466540424175732 + ], + [ + -0.09671952252964748, + -0.6656150108320557, + -0.059775952298983345 + ], + [ + -0.09671952252964748, + 0.6656150108320557, + -0.059775952298983345 + ] + ], + "symmetry_group": "[5,3]", + "short_code": "A07" + }, + "Truncated Icosahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.04264516389768866, + -0.5559768006576571, + 0.33493946561987653 + ], + [ + -0.04264516389768866, + 0.5559768006576571, + 0.33493946561987653 + ], + [ + 0.04264516389768866, + -0.5559768006576571, + -0.3349394656198766 + ], + [ + 0.04264516389768866, + 0.5559768006576571, + -0.3349394656198766 + ], + [ + -0.0690013246422702, + -0.21236424089480008, + -0.6109447641889573 + ], + [ + -0.0690013246422702, + -0.6370927226844003, + -0.11164648853995886 + ], + [ + -0.0690013246422702, + 0.2123642408948001, + -0.6109447641889573 + ], + [ + -0.0690013246422702, + 0.6370927226844003, + -0.11164648853995886 + ], + [ + 0.0690013246422702, + -0.21236424089480008, + 0.6109447641889573 + ], + [ + 0.0690013246422702, + -0.6370927226844003, + 0.11164648853995884 + ], + [ + 0.0690013246422702, + 0.2123642408948001, + 0.6109447641889573 + ], + [ + 0.0690013246422702, + 0.6370927226844003, + 0.11164648853995884 + ], + [ + 0.18064781318222906, + -0.13124831886805685, + -0.6109447641889573 + ], + [ + 0.18064781318222906, + 0.13124831886805685, + -0.6109447641889573 + ], + [ + 0.3186504624667694, + -0.5559768006576571, + 0.11164648853995884 + ], + [ + 0.3186504624667694, + 0.5559768006576571, + 0.11164648853995884 + ], + [ + -0.5419434395466872, + -0.13124831886805685, + 0.33493946561987653 + ], + [ + -0.5419434395466872, + 0.13124831886805685, + 0.33493946561987653 + ], + [ + -0.3612956263644581, + -0.2624966377361137, + 0.47294211490441695 + ], + [ + -0.3612956263644581, + 0.2624966377361137, + 0.47294211490441695 + ], + [ + -0.3612956263644581, + -0.42472848178960015, + -0.3349394656198766 + ], + [ + -0.3612956263644581, + 0.4247284817896002, + -0.3349394656198766 + ], + [ + -0.18064781318222906, + -0.13124831886805685, + 0.6109447641889573 + ], + [ + -0.18064781318222906, + 0.13124831886805685, + 0.6109447641889573 + ], + [ + 0.3612956263644581, + -0.2624966377361137, + -0.47294211490441695 + ], + [ + 0.3612956263644581, + 0.2624966377361137, + -0.47294211490441695 + ], + [ + 0.3612956263644581, + -0.42472848178960015, + 0.33493946561987653 + ], + [ + 0.3612956263644581, + 0.4247284817896002, + 0.33493946561987653 + ], + [ + -0.4465859541598354, + 0.0, + -0.47294211490441695 + ], + [ + 0.4465859541598354, + 0.0, + 0.47294211490441695 + ], + [ + -0.3186504624667694, + -0.5559768006576571, + -0.11164648853995886 + ], + [ + -0.3186504624667694, + 0.5559768006576571, + -0.11164648853995886 + ], + [ + -0.5155872788021056, + -0.21236424089480008, + -0.3349394656198766 + ], + [ + -0.5155872788021056, + 0.2123642408948001, + -0.3349394656198766 + ], + [ + 0.5419434395466872, + -0.13124831886805685, + -0.3349394656198766 + ], + [ + 0.5419434395466872, + 0.13124831886805685, + -0.3349394656198766 + ], + [ + 0.5845886034443758, + -0.2624966377361137, + -0.11164648853995886 + ], + [ + 0.5845886034443758, + 0.2624966377361137, + -0.11164648853995886 + ], + [ + 0.6272337673420644, + -0.13124831886805685, + 0.11164648853995884 + ], + [ + 0.6272337673420644, + 0.13124831886805685, + 0.11164648853995884 + ], + [ + -0.2922943017221879, + -0.4748608786309138, + 0.33493946561987653 + ], + [ + -0.2922943017221879, + 0.4748608786309138, + 0.33493946561987653 + ], + [ + 0.2922943017221879, + -0.4748608786309138, + -0.3349394656198766 + ], + [ + 0.2922943017221879, + 0.4748608786309138, + -0.3349394656198766 + ], + [ + -0.6272337673420644, + -0.13124831886805685, + -0.11164648853995886 + ], + [ + -0.6272337673420644, + 0.13124831886805685, + -0.11164648853995886 + ], + [ + -0.43029695100672827, + -0.4748608786309138, + 0.11164648853995884 + ], + [ + -0.43029695100672827, + 0.4748608786309138, + 0.11164648853995884 + ], + [ + 0.43029695100672827, + -0.4748608786309138, + -0.11164648853995886 + ], + [ + 0.43029695100672827, + 0.4748608786309138, + -0.11164648853995886 + ], + [ + 0.5155872788021056, + -0.21236424089480008, + 0.33493946561987653 + ], + [ + 0.5155872788021056, + 0.2123642408948001, + 0.33493946561987653 + ], + [ + 0.22329297707991771, + 0.0, + 0.6109447641889573 + ], + [ + -0.5845886034443758, + -0.2624966377361137, + 0.11164648853995884 + ], + [ + -0.5845886034443758, + 0.2624966377361137, + 0.11164648853995884 + ], + [ + -0.22329297707991771, + 0.0, + -0.6109447641889573 + ], + [ + -0.1380026492845404, + -0.42472848178960015, + -0.47294211490441695 + ], + [ + -0.1380026492845404, + 0.4247284817896002, + -0.47294211490441695 + ], + [ + 0.1380026492845404, + -0.42472848178960015, + 0.47294211490441695 + ], + [ + 0.1380026492845404, + 0.4247284817896002, + 0.47294211490441695 + ] + ], + "symmetry_group": "[5,3]", + "short_code": "A06" + }, + "Truncated Octahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.6681740386052545, + -0.22272467953508482, + 0.0 + ], + [ + -0.6681740386052545, + 0.22272467953508482, + 0.0 + ], + [ + -0.44544935907016964, + -0.44544935907016964, + -0.31498026247371824 + ], + [ + -0.44544935907016964, + -0.44544935907016964, + 0.31498026247371824 + ], + [ + -0.44544935907016964, + 0.44544935907016964, + -0.31498026247371824 + ], + [ + -0.44544935907016964, + 0.44544935907016964, + 0.31498026247371824 + ], + [ + -0.22272467953508482, + -0.6681740386052545, + 0.0 + ], + [ + -0.22272467953508482, + -0.22272467953508482, + -0.6299605249474366 + ], + [ + -0.22272467953508482, + -0.22272467953508482, + 0.6299605249474366 + ], + [ + -0.22272467953508482, + 0.22272467953508482, + -0.6299605249474366 + ], + [ + -0.22272467953508482, + 0.22272467953508482, + 0.6299605249474366 + ], + [ + -0.22272467953508482, + 0.6681740386052545, + 0.0 + ], + [ + 0.22272467953508482, + -0.6681740386052545, + 0.0 + ], + [ + 0.22272467953508482, + -0.22272467953508482, + -0.6299605249474366 + ], + [ + 0.22272467953508482, + -0.22272467953508482, + 0.6299605249474366 + ], + [ + 0.22272467953508482, + 0.22272467953508482, + -0.6299605249474366 + ], + [ + 0.22272467953508482, + 0.22272467953508482, + 0.6299605249474366 + ], + [ + 0.22272467953508482, + 0.6681740386052545, + 0.0 + ], + [ + 0.44544935907016964, + -0.44544935907016964, + -0.31498026247371824 + ], + [ + 0.44544935907016964, + -0.44544935907016964, + 0.31498026247371824 + ], + [ + 0.44544935907016964, + 0.44544935907016964, + -0.31498026247371824 + ], + [ + 0.44544935907016964, + 0.44544935907016964, + 0.31498026247371824 + ], + [ + 0.6681740386052545, + -0.22272467953508482, + 0.0 + ], + [ + 0.6681740386052545, + 0.22272467953508482, + 0.0 + ] + ], + "symmetry_group": "[4,3]", + "short_code": "A04" + }, + "Truncated Tetrahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.7172096715866663, + -0.43919943349410767 + ], + [ + 0.0, + 0.7172096715866663, + -0.43919943349410767 + ], + [ + -0.4140811969559649, + -0.7172096715866663, + 0.14639981116470258 + ], + [ + -0.4140811969559649, + 0.7172096715866663, + 0.14639981116470258 + ], + [ + -0.20704059847798245, + -0.35860483579333313, + 0.7319990558235129 + ], + [ + -0.20704059847798245, + 0.35860483579333313, + 0.7319990558235129 + ], + [ + 0.4140811969559649, + 0.0, + 0.7319990558235129 + ], + [ + 0.8281623939119298, + 0.0, + 0.14639981116470258 + ], + [ + -0.6211217954339473, + -0.35860483579333313, + -0.43919943349410767 + ], + [ + -0.6211217954339473, + 0.35860483579333313, + -0.43919943349410767 + ], + [ + 0.6211217954339473, + -0.35860483579333313, + -0.43919943349410767 + ], + [ + 0.6211217954339473, + 0.35860483579333313, + -0.43919943349410767 + ] + ], + "symmetry_group": "[3,3]", + "short_code": "A03" + } +} diff --git a/coxeter/families/data/catalan.json b/coxeter/families/data/catalan.json new file mode 100644 index 00000000..b7036ccf --- /dev/null +++ b/coxeter/families/data/catalan.json @@ -0,0 +1,2353 @@ +{ + "Deltoidal Hexecontahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + 0.0, + -0.6419842416261159 + ], + [ + 0.0, + 0.0, + 0.6419842416261159 + ], + [ + 0.0, + -0.6419842416261159, + 0.0 + ], + [ + 0.0, + 0.6419842416261159, + 0.0 + ], + [ + 0.0, + -0.560245521606332, + -0.3462507743976267 + ], + [ + 0.0, + -0.560245521606332, + 0.3462507743976267 + ], + [ + 0.0, + -0.22493388435932044, + -0.5888845544742393 + ], + [ + 0.0, + -0.22493388435932044, + 0.5888845544742393 + ], + [ + 0.0, + 0.22493388435932044, + -0.5888845544742393 + ], + [ + 0.0, + 0.22493388435932044, + 0.5888845544742393 + ], + [ + 0.0, + 0.560245521606332, + -0.3462507743976267 + ], + [ + 0.0, + 0.560245521606332, + 0.3462507743976267 + ], + [ + -0.6419842416261159, + 0.0, + 0.0 + ], + [ + -0.32099212081305784, + -0.5193761615964401, + 0.1983840407833823 + ], + [ + -0.32099212081305784, + -0.5193761615964401, + -0.1983840407833823 + ], + [ + -0.32099212081305784, + 0.5193761615964401, + 0.1983840407833823 + ], + [ + -0.32099212081305784, + 0.5193761615964401, + -0.1983840407833823 + ], + [ + 0.32099212081305784, + -0.5193761615964401, + 0.1983840407833823 + ], + [ + 0.32099212081305784, + -0.5193761615964401, + -0.1983840407833823 + ], + [ + 0.32099212081305784, + 0.5193761615964401, + 0.1983840407833823 + ], + [ + 0.32099212081305784, + 0.5193761615964401, + -0.1983840407833823 + ], + [ + 0.6419842416261159, + 0.0, + 0.0 + ], + [ + -0.5888845544742393, + 0.0, + -0.22493388435932044 + ], + [ + -0.5888845544742393, + 0.0, + 0.22493388435932044 + ], + [ + -0.36395067011491883, + -0.36395067011491883, + -0.36395067011491883 + ], + [ + -0.36395067011491883, + -0.36395067011491883, + 0.36395067011491883 + ], + [ + -0.36395067011491883, + 0.36395067011491883, + -0.36395067011491883 + ], + [ + -0.36395067011491883, + 0.36395067011491883, + 0.36395067011491883 + ], + [ + -0.560245521606332, + -0.3462507743976267, + 0.0 + ], + [ + -0.560245521606332, + 0.3462507743976267, + 0.0 + ], + [ + -0.22493388435932044, + -0.5888845544742393, + 0.0 + ], + [ + -0.22493388435932044, + 0.5888845544742393, + 0.0 + ], + [ + -0.3462507743976267, + 0.0, + -0.560245521606332 + ], + [ + -0.3462507743976267, + 0.0, + 0.560245521606332 + ], + [ + -0.5193761615964401, + 0.1983840407833823, + -0.32099212081305784 + ], + [ + -0.5193761615964401, + 0.1983840407833823, + 0.32099212081305784 + ], + [ + -0.5193761615964401, + -0.1983840407833823, + -0.32099212081305784 + ], + [ + -0.5193761615964401, + -0.1983840407833823, + 0.32099212081305784 + ], + [ + 0.1983840407833823, + -0.32099212081305784, + -0.5193761615964401 + ], + [ + 0.1983840407833823, + -0.32099212081305784, + 0.5193761615964401 + ], + [ + 0.1983840407833823, + 0.32099212081305784, + -0.5193761615964401 + ], + [ + 0.1983840407833823, + 0.32099212081305784, + 0.5193761615964401 + ], + [ + -0.1983840407833823, + -0.32099212081305784, + -0.5193761615964401 + ], + [ + -0.1983840407833823, + -0.32099212081305784, + 0.5193761615964401 + ], + [ + -0.1983840407833823, + 0.32099212081305784, + -0.5193761615964401 + ], + [ + -0.1983840407833823, + 0.32099212081305784, + 0.5193761615964401 + ], + [ + 0.3462507743976267, + 0.0, + -0.560245521606332 + ], + [ + 0.3462507743976267, + 0.0, + 0.560245521606332 + ], + [ + 0.5193761615964401, + 0.1983840407833823, + -0.32099212081305784 + ], + [ + 0.5193761615964401, + 0.1983840407833823, + 0.32099212081305784 + ], + [ + 0.5193761615964401, + -0.1983840407833823, + -0.32099212081305784 + ], + [ + 0.5193761615964401, + -0.1983840407833823, + 0.32099212081305784 + ], + [ + 0.22493388435932044, + -0.5888845544742393, + 0.0 + ], + [ + 0.22493388435932044, + 0.5888845544742393, + 0.0 + ], + [ + 0.560245521606332, + -0.3462507743976267, + 0.0 + ], + [ + 0.560245521606332, + 0.3462507743976267, + 0.0 + ], + [ + 0.36395067011491883, + -0.36395067011491883, + -0.36395067011491883 + ], + [ + 0.36395067011491883, + -0.36395067011491883, + 0.36395067011491883 + ], + [ + 0.36395067011491883, + 0.36395067011491883, + -0.36395067011491883 + ], + [ + 0.36395067011491883, + 0.36395067011491883, + 0.36395067011491883 + ], + [ + 0.5888845544742393, + 0.0, + -0.22493388435932044 + ], + [ + 0.5888845544742393, + 0.0, + 0.22493388435932044 + ] + ], + "symmetry_group": "[5,3]", + "short_code": "C09" + }, + "Deltoidal Icositetrahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.48527273468286136, + -0.48527273468286136, + 0.0 + ], + [ + -0.48527273468286136, + 0.0, + -0.48527273468286136 + ], + [ + -0.48527273468286136, + 0.0, + 0.48527273468286136 + ], + [ + -0.48527273468286136, + 0.48527273468286136, + 0.0 + ], + [ + 0.0, + -0.48527273468286136, + -0.48527273468286136 + ], + [ + 0.0, + -0.48527273468286136, + 0.48527273468286136 + ], + [ + 0.0, + 0.0, + -0.6862792828383832 + ], + [ + 0.0, + 0.0, + 0.6862792828383832 + ], + [ + 0.0, + 0.48527273468286136, + -0.48527273468286136 + ], + [ + 0.0, + 0.48527273468286136, + 0.48527273468286136 + ], + [ + 0.0, + -0.6862792828383832, + 0.0 + ], + [ + 0.0, + 0.6862792828383832, + 0.0 + ], + [ + 0.48527273468286136, + -0.48527273468286136, + 0.0 + ], + [ + 0.48527273468286136, + 0.0, + -0.48527273468286136 + ], + [ + 0.48527273468286136, + 0.0, + 0.48527273468286136 + ], + [ + 0.48527273468286136, + 0.48527273468286136, + 0.0 + ], + [ + -0.6862792828383832, + 0.0, + 0.0 + ], + [ + 0.6862792828383832, + 0.0, + 0.0 + ], + [ + 0.3753386030814041, + 0.3753386030814041, + 0.3753386030814041 + ], + [ + 0.3753386030814041, + 0.3753386030814041, + -0.3753386030814041 + ], + [ + 0.3753386030814041, + -0.3753386030814041, + 0.3753386030814041 + ], + [ + 0.3753386030814041, + -0.3753386030814041, + -0.3753386030814041 + ], + [ + -0.3753386030814041, + 0.3753386030814041, + 0.3753386030814041 + ], + [ + -0.3753386030814041, + 0.3753386030814041, + -0.3753386030814041 + ], + [ + -0.3753386030814041, + -0.3753386030814041, + 0.3753386030814041 + ], + [ + -0.3753386030814041, + -0.3753386030814041, + -0.3753386030814041 + ] + ], + "symmetry_group": "[4,3]", + "short_code": "C08" + }, + "Disdyakis Dodecahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + 0.4463719408331803, + 0.4463719408331803 + ], + [ + 0.0, + -0.4463719408331803, + -0.4463719408331803 + ], + [ + 0.0, + 0.4463719408331803, + -0.4463719408331803 + ], + [ + 0.0, + -0.4463719408331803, + 0.4463719408331803 + ], + [ + 0.4463719408331803, + 0.0, + 0.4463719408331803 + ], + [ + 0.4463719408331803, + 0.4463719408331803, + 0.0 + ], + [ + 0.38474083691454564, + 0.38474083691454564, + 0.38474083691454564 + ], + [ + -0.38474083691454564, + -0.38474083691454564, + -0.38474083691454564 + ], + [ + -0.4463719408331803, + 0.0, + -0.4463719408331803 + ], + [ + -0.4463719408331803, + -0.4463719408331803, + 0.0 + ], + [ + 0.38474083691454564, + 0.38474083691454564, + -0.38474083691454564 + ], + [ + 0.38474083691454564, + -0.38474083691454564, + 0.38474083691454564 + ], + [ + -0.38474083691454564, + 0.38474083691454564, + 0.38474083691454564 + ], + [ + 0.38474083691454564, + -0.38474083691454564, + -0.38474083691454564 + ], + [ + -0.38474083691454564, + 0.38474083691454564, + -0.38474083691454564 + ], + [ + -0.38474083691454564, + -0.38474083691454564, + 0.38474083691454564 + ], + [ + 0.4463719408331803, + 0.0, + -0.4463719408331803 + ], + [ + 0.4463719408331803, + -0.4463719408331803, + 0.0 + ], + [ + -0.4463719408331803, + 0.0, + 0.4463719408331803 + ], + [ + -0.4463719408331803, + 0.4463719408331803, + 0.0 + ], + [ + -0.7278549515601268, + 0.0, + 0.0 + ], + [ + 0.0, + -0.7278549515601268, + 0.0 + ], + [ + 0.0, + 0.0, + -0.7278549515601268 + ], + [ + 0.7278549515601268, + 0.0, + 0.0 + ], + [ + 0.0, + 0.7278549515601268, + 0.0 + ], + [ + 0.0, + 0.0, + 0.7278549515601268 + ] + ], + "symmetry_group": "[4,3]", + "short_code": "C10" + }, + "Disdyakis Triacontahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + 0.0, + -0.6223468916733766 + ], + [ + 0.0, + 0.0, + 0.6223468916733766 + ], + [ + 0.0, + -0.6223468916733766, + 0.0 + ], + [ + 0.0, + 0.6223468916733766, + 0.0 + ], + [ + 0.0, + -0.22615462529607505, + -0.5920804957381212 + ], + [ + 0.0, + 0.22615462529607505, + -0.5920804957381212 + ], + [ + 0.0, + -0.22615462529607505, + 0.5920804957381212 + ], + [ + 0.0, + 0.22615462529607505, + 0.5920804957381212 + ], + [ + -0.6223468916733766, + 0.0, + 0.0 + ], + [ + 0.6223468916733766, + 0.0, + 0.0 + ], + [ + -0.3659258704420462, + -0.3659258704420462, + -0.3659258704420462 + ], + [ + 0.3659258704420462, + 0.3659258704420462, + 0.3659258704420462 + ], + [ + -0.5920804957381212, + 0.0, + -0.22615462529607505 + ], + [ + -0.22615462529607505, + -0.5920804957381212, + 0.0 + ], + [ + -0.19231576592349786, + -0.3111734458366883, + -0.5034892117601861 + ], + [ + -0.5034892117601861, + -0.19231576592349786, + -0.3111734458366883 + ], + [ + -0.3111734458366883, + -0.5034892117601861, + -0.19231576592349786 + ], + [ + -0.19231576592349786, + 0.3111734458366883, + -0.5034892117601861 + ], + [ + -0.5034892117601861, + -0.19231576592349786, + 0.3111734458366883 + ], + [ + 0.3111734458366883, + -0.5034892117601861, + -0.19231576592349786 + ], + [ + -0.5920804957381212, + 0.0, + 0.22615462529607505 + ], + [ + 0.22615462529607505, + -0.5920804957381212, + 0.0 + ], + [ + -0.3552482974428728, + 0.0, + -0.5748038197081005 + ], + [ + -0.5748038197081005, + -0.3552482974428728, + 0.0 + ], + [ + 0.0, + -0.5748038197081005, + -0.3552482974428728 + ], + [ + -0.5034892117601861, + 0.19231576592349786, + -0.3111734458366883 + ], + [ + -0.3111734458366883, + -0.5034892117601861, + 0.19231576592349786 + ], + [ + 0.19231576592349786, + -0.3111734458366883, + -0.5034892117601861 + ], + [ + -0.5034892117601861, + 0.19231576592349786, + 0.3111734458366883 + ], + [ + 0.3111734458366883, + -0.5034892117601861, + 0.19231576592349786 + ], + [ + 0.19231576592349786, + 0.3111734458366883, + -0.5034892117601861 + ], + [ + -0.5748038197081005, + 0.3552482974428728, + 0.0 + ], + [ + 0.0, + -0.5748038197081005, + 0.3552482974428728 + ], + [ + 0.3552482974428728, + 0.0, + -0.5748038197081005 + ], + [ + -0.3659258704420462, + -0.3659258704420462, + 0.3659258704420462 + ], + [ + -0.3659258704420462, + 0.3659258704420462, + -0.3659258704420462 + ], + [ + 0.3659258704420462, + -0.3659258704420462, + -0.3659258704420462 + ], + [ + -0.3659258704420462, + 0.3659258704420462, + 0.3659258704420462 + ], + [ + 0.3659258704420462, + -0.3659258704420462, + 0.3659258704420462 + ], + [ + 0.3659258704420462, + 0.3659258704420462, + -0.3659258704420462 + ], + [ + -0.19231576592349786, + -0.3111734458366883, + 0.5034892117601861 + ], + [ + -0.3111734458366883, + 0.5034892117601861, + -0.19231576592349786 + ], + [ + 0.5034892117601861, + -0.19231576592349786, + -0.3111734458366883 + ], + [ + -0.19231576592349786, + 0.3111734458366883, + 0.5034892117601861 + ], + [ + 0.3111734458366883, + 0.5034892117601861, + -0.19231576592349786 + ], + [ + 0.5034892117601861, + -0.19231576592349786, + 0.3111734458366883 + ], + [ + -0.3111734458366883, + 0.5034892117601861, + 0.19231576592349786 + ], + [ + 0.19231576592349786, + -0.3111734458366883, + 0.5034892117601861 + ], + [ + 0.5034892117601861, + 0.19231576592349786, + -0.3111734458366883 + ], + [ + 0.3111734458366883, + 0.5034892117601861, + 0.19231576592349786 + ], + [ + 0.19231576592349786, + 0.3111734458366883, + 0.5034892117601861 + ], + [ + 0.5034892117601861, + 0.19231576592349786, + 0.3111734458366883 + ], + [ + -0.22615462529607505, + 0.5920804957381212, + 0.0 + ], + [ + 0.5920804957381212, + 0.0, + -0.22615462529607505 + ], + [ + 0.22615462529607505, + 0.5920804957381212, + 0.0 + ], + [ + 0.5920804957381212, + 0.0, + 0.22615462529607505 + ], + [ + -0.3552482974428728, + 0.0, + 0.5748038197081005 + ], + [ + 0.0, + 0.5748038197081005, + -0.3552482974428728 + ], + [ + 0.5748038197081005, + -0.3552482974428728, + 0.0 + ], + [ + 0.0, + 0.5748038197081005, + 0.3552482974428728 + ], + [ + 0.3552482974428728, + 0.0, + 0.5748038197081005 + ], + [ + 0.5748038197081005, + 0.3552482974428728, + 0.0 + ] + ], + "symmetry_group": "[5,3]", + "short_code": "C11" + }, + "Pentagonal Hexecontahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + 0.0, + -0.6320419117354957 + ], + [ + 0.0, + 0.0, + 0.6320419117354957 + ], + [ + -0.42136127449033045, + 0.0, + -0.47109622642316346 + ], + [ + 0.42136127449033045, + 0.0, + 0.47109622642316346 + ], + [ + -0.6509621851044832, + 0.0, + -0.12432271465950603 + ], + [ + 0.6509621851044832, + 0.0, + 0.12432271465950603 + ], + [ + -0.4023167557854712, + 0.0, + 0.5266394704449772 + ], + [ + 0.4023167557854712, + 0.0, + -0.5266394704449772 + ], + [ + -0.5174872356870693, + 0.21742688711526248, + -0.29053310973206226 + ], + [ + 0.5174872356870693, + 0.21742688711526248, + 0.29053310973206226 + ], + [ + -0.5574134719305179, + -0.2865811568439133, + -0.08147662267565 + ], + [ + 0.5574134719305179, + -0.2865811568439133, + 0.08147662267565 + ], + [ + -0.5031037402276166, + -0.11189395888813491, + -0.3658460697118166 + ], + [ + 0.5031037402276166, + -0.11189395888813491, + 0.3658460697118166 + ], + [ + -0.5806864564609423, + 0.2462711651934537, + 0.04038230636495313 + ], + [ + 0.5806864564609423, + 0.2462711651934537, + -0.04038230636495313 + ], + [ + -0.6053622275022513, + -0.06522293657666803, + 0.16958632093446835 + ], + [ + 0.6053622275022513, + -0.06522293657666803, + -0.16958632093446835 + ], + [ + -0.03052017389249741, + 0.6260248055254692, + 0.08147662267565 + ], + [ + 0.03052017389249741, + 0.6260248055254692, + -0.08147662267565 + ], + [ + -0.47109622642316346, + -0.3649095678796141, + -0.21068063724516523 + ], + [ + -0.47109622642316346, + 0.3649095678796141, + -0.21068063724516523 + ], + [ + 0.47109622642316346, + -0.3649095678796141, + 0.21068063724516523 + ], + [ + 0.47109622642316346, + 0.3649095678796141, + 0.21068063724516523 + ], + [ + -0.4287634236493464, + 0.16947772050002047, + -0.43233807024696336 + ], + [ + 0.4287634236493464, + 0.16947772050002047, + 0.43233807024696336 + ], + [ + -0.5642679111915545, + 0.06522293657666803, + 0.2771726377803119 + ], + [ + 0.5642679111915545, + 0.06522293657666803, + -0.2771726377803119 + ], + [ + -0.5268932980380205, + -0.33944364868155597, + 0.08147662267565 + ], + [ + 0.5268932980380205, + -0.33944364868155597, + -0.08147662267565 + ], + [ + -0.5036203135075961, + 0.37975364033201553, + -0.04038230636495313 + ], + [ + 0.5036203135075961, + 0.37975364033201553, + 0.04038230636495313 + ], + [ + -0.5515690690793296, + -0.22552651576963842, + 0.21068063724516523 + ], + [ + -0.5515690690793296, + 0.22552651576963842, + 0.21068063724516523 + ], + [ + 0.5515690690793296, + -0.22552651576963842, + -0.21068063724516523 + ], + [ + 0.5515690690793296, + 0.22552651576963842, + -0.21068063724516523 + ], + [ + -0.4431469191087991, + -0.2750106487271481, + -0.35702511026720896 + ], + [ + 0.4431469191087991, + -0.2750106487271481, + 0.35702511026720896 + ], + [ + -0.13109400781990432, + 0.11189395888813491, + 0.6080880538773273 + ], + [ + 0.13109400781990432, + 0.11189395888813491, + -0.6080880538773273 + ], + [ + -0.07706614295334618, + -0.6260248055254692, + -0.04038230636495313 + ], + [ + 0.07706614295334618, + -0.6260248055254692, + 0.04038230636495313 + ], + [ + -0.07044641013594592, + -0.5568705357968184, + 0.29053310973206226 + ], + [ + 0.07044641013594592, + -0.5568705357968184, + -0.29053310973206226 + ], + [ + -0.19202347234020592, + -0.21742688711526248, + 0.5615420848164785 + ], + [ + 0.19202347234020592, + -0.21742688711526248, + -0.5615420848164785 + ], + [ + -0.0804728426561661, + -0.5904360836492526, + -0.21068063724516523 + ], + [ + -0.0804728426561661, + 0.5904360836492526, + -0.21068063724516523 + ], + [ + 0.0804728426561661, + -0.5904360836492526, + 0.21068063724516523 + ], + [ + 0.0804728426561661, + 0.5904360836492526, + 0.21068063724516523 + ], + [ + -0.09228547153748583, + 0.2750106487271481, + 0.5615420848164785 + ], + [ + 0.09228547153748583, + 0.2750106487271481, + -0.5615420848164785 + ], + [ + -0.06760970049617672, + -0.45605887734393374, + 0.43233807024696336 + ], + [ + 0.06760970049617672, + -0.45605887734393374, + -0.43233807024696336 + ], + [ + -0.45973966766334834, + -0.2462711651934537, + 0.35702511026720896 + ], + [ + 0.45973966766334834, + -0.2462711651934537, + -0.35702511026720896 + ], + [ + -0.016592748554549244, + 0.5212818139206018, + -0.35702511026720896 + ], + [ + 0.016592748554549244, + 0.5212818139206018, + 0.35702511026720896 + ], + [ + -0.3591658337359414, + -0.4916475992201504, + -0.16958632093446835 + ], + [ + 0.3591658337359414, + -0.4916475992201504, + 0.16958632093446835 + ], + [ + -0.3611537231531697, + 0.2865811568439133, + 0.43233807024696336 + ], + [ + 0.3611537231531697, + 0.2865811568439133, + -0.43233807024696336 + ], + [ + -0.031356007017184245, + -0.16947772050002047, + 0.6080880538773273 + ], + [ + 0.031356007017184245, + -0.16947772050002047, + -0.6080880538773273 + ], + [ + -0.15464885918667187, + 0.4916475992201504, + 0.3658460697118166 + ], + [ + 0.15464885918667187, + 0.4916475992201504, + -0.3658460697118166 + ], + [ + -0.44704082555112346, + 0.33944364868155597, + 0.29053310973206226 + ], + [ + 0.44704082555112346, + 0.33944364868155597, + -0.29053310973206226 + ], + [ + -0.21068063724516523, + -0.3649095678796141, + 0.47109622642316346 + ], + [ + -0.21068063724516523, + 0.3649095678796141, + 0.47109622642316346 + ], + [ + 0.21068063724516523, + -0.3649095678796141, + -0.47109622642316346 + ], + [ + 0.21068063724516523, + 0.3649095678796141, + -0.47109622642316346 + ], + [ + -0.22564923561096148, + -0.5212818139206018, + -0.2771726377803119 + ], + [ + 0.22564923561096148, + -0.5212818139206018, + 0.2771726377803119 + ], + [ + -0.33861867558059305, + 0.45605887734393374, + -0.2771726377803119 + ], + [ + 0.33861867558059305, + 0.45605887734393374, + 0.2771726377803119 + ], + [ + -0.24619639376630992, + 0.5568705357968184, + -0.16958632093446835 + ], + [ + 0.24619639376630992, + 0.5568705357968184, + 0.16958632093446835 + ], + [ + -0.2843089438776917, + -0.05758376161188555, + -0.5615420848164785 + ], + [ + 0.2843089438776917, + -0.05758376161188555, + 0.5615420848164785 + ], + [ + -0.3484548810409447, + -0.37975364033201553, + 0.3658460697118166 + ], + [ + 0.3484548810409447, + -0.37975364033201553, + -0.3658460697118166 + ], + [ + -0.1624500148370886, + 0.05758376161188555, + -0.6080880538773273 + ], + [ + 0.1624500148370886, + 0.05758376161188555, + 0.6080880538773273 + ], + [ + -0.3254810925522416, + -0.5637497892035106, + 0.12432271465950603 + ], + [ + -0.3254810925522416, + 0.5637497892035106, + 0.12432271465950603 + ], + [ + 0.3254810925522416, + -0.5637497892035106, + -0.12432271465950603 + ], + [ + 0.3254810925522416, + 0.5637497892035106, + -0.12432271465950603 + ], + [ + -0.2011583778927356, + -0.34841653087835806, + -0.5266394704449772 + ], + [ + -0.2011583778927356, + 0.34841653087835806, + -0.5266394704449772 + ], + [ + 0.2011583778927356, + -0.34841653087835806, + 0.5266394704449772 + ], + [ + 0.2011583778927356, + 0.34841653087835806, + 0.5266394704449772 + ] + ], + "symmetry_group": "[5,3]+", + "short_code": "C13" + }, + "Pentagonal Icositetrahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + 0.0, + -0.6971413634788861 + ], + [ + 0.0, + 0.0, + 0.6971413634788861 + ], + [ + 0.0, + -0.6971413634788861, + 0.0 + ], + [ + 0.0, + 0.6971413634788861, + 0.0 + ], + [ + -0.5241866771253695, + -0.3790280996166435, + -0.1120398505991157 + ], + [ + -0.5241866771253695, + 0.3790280996166435, + 0.11203985059911571 + ], + [ + -0.5241866771253695, + -0.1120398505991157, + 0.3790280996166435 + ], + [ + -0.5241866771253695, + 0.11203985059911571, + -0.3790280996166435 + ], + [ + 0.5241866771253695, + -0.3790280996166435, + 0.11203985059911571 + ], + [ + 0.5241866771253695, + 0.3790280996166435, + -0.1120398505991157 + ], + [ + 0.5241866771253695, + -0.1120398505991157, + -0.3790280996166435 + ], + [ + 0.5241866771253695, + 0.11203985059911571, + 0.3790280996166435 + ], + [ + -0.6971413634788861, + 0.0, + 0.0 + ], + [ + 0.6971413634788861, + 0.0, + 0.0 + ], + [ + -0.3790280996166435, + -0.5241866771253695, + 0.11203985059911571 + ], + [ + -0.3790280996166435, + 0.5241866771253695, + -0.1120398505991157 + ], + [ + -0.3790280996166435, + -0.3790280996166435, + -0.3790280996166435 + ], + [ + -0.3790280996166435, + -0.3790280996166435, + 0.3790280996166435 + ], + [ + -0.3790280996166435, + 0.3790280996166435, + -0.3790280996166435 + ], + [ + -0.3790280996166435, + 0.3790280996166435, + 0.3790280996166435 + ], + [ + -0.3790280996166435, + -0.1120398505991157, + -0.5241866771253695 + ], + [ + -0.3790280996166435, + 0.11203985059911571, + 0.5241866771253695 + ], + [ + 0.3790280996166435, + -0.5241866771253695, + -0.1120398505991157 + ], + [ + 0.3790280996166435, + 0.5241866771253695, + 0.11203985059911571 + ], + [ + 0.3790280996166435, + -0.3790280996166435, + -0.3790280996166435 + ], + [ + 0.3790280996166435, + -0.3790280996166435, + 0.3790280996166435 + ], + [ + 0.3790280996166435, + 0.3790280996166435, + -0.3790280996166435 + ], + [ + 0.3790280996166435, + 0.3790280996166435, + 0.3790280996166435 + ], + [ + 0.3790280996166435, + -0.1120398505991157, + 0.5241866771253695 + ], + [ + 0.3790280996166435, + 0.11203985059911571, + -0.5241866771253695 + ], + [ + -0.1120398505991157, + -0.5241866771253695, + -0.3790280996166435 + ], + [ + -0.1120398505991157, + 0.5241866771253695, + 0.3790280996166435 + ], + [ + -0.1120398505991157, + -0.3790280996166435, + 0.5241866771253695 + ], + [ + -0.1120398505991157, + 0.3790280996166435, + -0.5241866771253695 + ], + [ + 0.11203985059911571, + -0.5241866771253695, + 0.3790280996166435 + ], + [ + 0.11203985059911571, + 0.5241866771253695, + -0.3790280996166435 + ], + [ + 0.11203985059911571, + -0.3790280996166435, + -0.5241866771253695 + ], + [ + 0.11203985059911571, + 0.3790280996166435, + 0.5241866771253695 + ] + ], + "symmetry_group": "[4,3]+", + "short_code": "C12" + }, + "Pentakis Dodecahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.4031496965122191, + 0.0, + 0.5277298040115964 + ], + [ + 0.5786367243263828, + 0.0, + 0.2893183621631914 + ], + [ + 0.0, + 0.0, + 0.646935524935799 + ], + [ + -0.46812694354949513, + -0.3401141329938731, + 0.2893183621631914 + ], + [ + -0.46812694354949513, + 0.3401141329938731, + 0.2893183621631914 + ], + [ + 0.0, + 0.0, + -0.646935524935799 + ], + [ + 0.17880858138630382, + -0.5503162272382887, + 0.2893183621631914 + ], + [ + 0.17880858138630382, + 0.5503162272382887, + 0.2893183621631914 + ], + [ + -0.12458010749937797, + -0.3834181459103589, + 0.5277298040115964 + ], + [ + -0.12458010749937797, + 0.3834181459103589, + 0.5277298040115964 + ], + [ + 0.3261549557554872, + 0.2369654460760683, + 0.5277298040115964 + ], + [ + 0.3261549557554872, + -0.2369654460760683, + 0.5277298040115964 + ], + [ + 0.40314969651221844, + 0.0, + -0.5277298040115964 + ], + [ + 0.12458010749937797, + -0.3834181459103589, + -0.5277298040115964 + ], + [ + 0.12458010749937797, + 0.3834181459103589, + -0.5277298040115964 + ], + [ + -0.3261549557554872, + 0.2369654460760683, + -0.5277298040115964 + ], + [ + -0.3261549557554872, + -0.2369654460760683, + -0.5277298040115964 + ], + [ + 0.5277298040115964, + -0.3834181459103589, + 0.12458010749937797 + ], + [ + -0.20157484825610922, + -0.6203835919864272, + 0.12458010749937797 + ], + [ + 0.5277298040115964, + 0.3834181459103589, + 0.12458010749937797 + ], + [ + -0.20157484825610922, + 0.6203835919864272, + 0.12458010749937797 + ], + [ + -0.6523099115109744, + 0.0, + 0.12458010749937797 + ], + [ + 0.6523099115109744, + 0.0, + -0.12458010749937797 + ], + [ + 0.20157484825610922, + -0.6203835919864272, + -0.12458010749937797 + ], + [ + 0.20157484825610922, + 0.6203835919864272, + -0.12458010749937797 + ], + [ + -0.5277298040115964, + -0.3834181459103589, + -0.12458010749937797 + ], + [ + -0.5277298040115964, + 0.3834181459103589, + -0.12458010749937797 + ], + [ + 0.46812694354949513, + -0.3401141329938731, + -0.2893183621631914 + ], + [ + -0.5786367243263828, + 0.0, + -0.2893183621631914 + ], + [ + 0.46812694354949513, + 0.3401141329938731, + -0.2893183621631914 + ], + [ + -0.17880858138630382, + -0.5503162272382887, + -0.2893183621631914 + ], + [ + -0.17880858138630382, + 0.5503162272382887, + -0.2893183621631914 + ] + ], + "symmetry_group": "[5,3]", + "short_code": "C06" + }, + "Rhombic Dodecahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.5612310241546865, + -0.5612310241546865, + 0.0 + ], + [ + -0.5612310241546865, + 0.0, + -0.3968502629920499 + ], + [ + -0.5612310241546865, + 0.0, + 0.3968502629920499 + ], + [ + -0.5612310241546865, + 0.5612310241546865, + 0.0 + ], + [ + 0.0, + -0.5612310241546865, + -0.3968502629920499 + ], + [ + 0.0, + -0.5612310241546865, + 0.3968502629920499 + ], + [ + 0.0, + 0.0, + -0.7937005259840998 + ], + [ + 0.0, + 0.0, + 0.7937005259840998 + ], + [ + 0.0, + 0.5612310241546865, + -0.3968502629920499 + ], + [ + 0.0, + 0.5612310241546865, + 0.3968502629920499 + ], + [ + 0.5612310241546865, + -0.5612310241546865, + 0.0 + ], + [ + 0.5612310241546865, + 0.0, + -0.3968502629920499 + ], + [ + 0.5612310241546865, + 0.0, + 0.3968502629920499 + ], + [ + 0.5612310241546865, + 0.5612310241546865, + 0.0 + ] + ], + "symmetry_group": "[4,3]", + "short_code": "C01" + }, + "Rhombic Triacontahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + 0.0, + -0.7007444326037079 + ], + [ + 0.0, + 0.0, + 0.7007444326037079 + ], + [ + 0.11970143954506929, + -0.36840314986403866, + 0.5070634349174951 + ], + [ + 0.11970143954506929, + 0.36840314986403866, + 0.5070634349174951 + ], + [ + 0.3873619953724257, + 0.0, + 0.5070634349174951 + ], + [ + 0.5070634349174951, + -0.36840314986403866, + 0.3133824372312822 + ], + [ + 0.5070634349174951, + -0.36840314986403866, + -0.11970143954506929 + ], + [ + 0.5070634349174951, + 0.36840314986403866, + 0.3133824372312822 + ], + [ + 0.5070634349174951, + 0.36840314986403866, + -0.11970143954506929 + ], + [ + -0.3873619953724257, + 0.0, + -0.5070634349174951 + ], + [ + -0.19368099768621286, + -0.5960888180425357, + 0.3133824372312822 + ], + [ + -0.19368099768621286, + -0.5960888180425357, + -0.11970143954506929 + ], + [ + -0.19368099768621286, + 0.5960888180425357, + 0.3133824372312822 + ], + [ + -0.19368099768621286, + 0.5960888180425357, + -0.11970143954506929 + ], + [ + 0.19368099768621286, + -0.5960888180425357, + 0.11970143954506929 + ], + [ + 0.19368099768621286, + -0.5960888180425357, + -0.3133824372312822 + ], + [ + 0.19368099768621286, + 0.5960888180425357, + 0.11970143954506929 + ], + [ + 0.19368099768621286, + 0.5960888180425357, + -0.3133824372312822 + ], + [ + -0.6267648744625643, + 0.0, + 0.3133824372312822 + ], + [ + -0.6267648744625643, + 0.0, + -0.11970143954506929 + ], + [ + -0.3133824372312822, + -0.22768566817849706, + 0.5070634349174951 + ], + [ + -0.3133824372312822, + 0.22768566817849706, + 0.5070634349174951 + ], + [ + 0.3133824372312822, + -0.22768566817849706, + -0.5070634349174951 + ], + [ + 0.3133824372312822, + 0.22768566817849706, + -0.5070634349174951 + ], + [ + 0.6267648744625643, + 0.0, + 0.11970143954506929 + ], + [ + 0.6267648744625643, + 0.0, + -0.3133824372312822 + ], + [ + -0.5070634349174951, + -0.36840314986403866, + 0.11970143954506929 + ], + [ + -0.5070634349174951, + -0.36840314986403866, + -0.3133824372312822 + ], + [ + -0.5070634349174951, + 0.36840314986403866, + 0.11970143954506929 + ], + [ + -0.5070634349174951, + 0.36840314986403866, + -0.3133824372312822 + ], + [ + -0.11970143954506929, + -0.36840314986403866, + -0.5070634349174951 + ], + [ + -0.11970143954506929, + 0.36840314986403866, + -0.5070634349174951 + ] + ], + "symmetry_group": "[5,3]", + "short_code": "C02" + }, + "Triakis Octahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.35004956798230363, + -0.35004956798230363, + -0.35004956798230363 + ], + [ + -0.35004956798230363, + -0.35004956798230363, + 0.35004956798230363 + ], + [ + -0.35004956798230363, + 0.35004956798230363, + -0.35004956798230363 + ], + [ + -0.35004956798230363, + 0.35004956798230363, + 0.35004956798230363 + ], + [ + 0.0, + 0.0, + -0.8450944145257201 + ], + [ + 0.0, + 0.0, + 0.8450944145257201 + ], + [ + 0.0, + -0.8450944145257201, + 0.0 + ], + [ + 0.0, + 0.8450944145257201, + 0.0 + ], + [ + 0.35004956798230363, + -0.35004956798230363, + -0.35004956798230363 + ], + [ + 0.35004956798230363, + -0.35004956798230363, + 0.35004956798230363 + ], + [ + 0.35004956798230363, + 0.35004956798230363, + -0.35004956798230363 + ], + [ + 0.35004956798230363, + 0.35004956798230363, + 0.35004956798230363 + ], + [ + -0.8450944145257201, + 0.0, + 0.0 + ], + [ + 0.8450944145257201, + 0.0, + 0.0 + ] + ], + "symmetry_group": "[4,3]", + "short_code": "C05" + }, + "Tetrakis Hexahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.6177146705271326, + 0.0, + -0.43679023236814946 + ], + [ + -0.6177146705271326, + 0.0, + 0.43679023236814946 + ], + [ + -0.46328600289534944, + -0.46328600289534944, + 0.0 + ], + [ + -0.46328600289534944, + 0.46328600289534944, + 0.0 + ], + [ + 0.0, + -0.6177146705271326, + -0.43679023236814946 + ], + [ + 0.0, + -0.6177146705271326, + 0.43679023236814946 + ], + [ + 0.0, + 0.0, + -0.6551853485522242 + ], + [ + 0.0, + 0.0, + 0.6551853485522242 + ], + [ + 0.0, + 0.6177146705271326, + -0.43679023236814946 + ], + [ + 0.0, + 0.6177146705271326, + 0.43679023236814946 + ], + [ + 0.46328600289534944, + -0.46328600289534944, + 0.0 + ], + [ + 0.46328600289534944, + 0.46328600289534944, + 0.0 + ], + [ + 0.6177146705271326, + 0.0, + -0.43679023236814946 + ], + [ + 0.6177146705271326, + 0.0, + 0.43679023236814946 + ] + ], + "symmetry_group": "[4,3]", + "short_code": "C04" + }, + "Triakis Icosahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + 0.0, + 0.7156651049150559 + ], + [ + 0.11476223599505815, + -0.3532018444114118, + 0.48614063292493953 + ], + [ + 0.11476223599505815, + 0.3532018444114118, + 0.48614063292493953 + ], + [ + 0.37137839692988145, + 0.0, + 0.48614063292493953 + ], + [ + 0.0, + 0.0, + -0.7156651049150559 + ], + [ + -0.11476223599505815, + -0.3532018444114118, + -0.48614063292493953 + ], + [ + -0.11476223599505815, + 0.3532018444114118, + -0.48614063292493953 + ], + [ + 0.3004514344599989, + -0.21829074473540458, + -0.48614063292493953 + ], + [ + 0.3004514344599989, + 0.21829074473540458, + -0.48614063292493953 + ], + [ + -0.37137839692988145, + 0.0, + -0.48614063292493953 + ], + [ + -0.3004514344599989, + -0.21829074473540458, + 0.48614063292493953 + ], + [ + -0.3004514344599989, + 0.21829074473540458, + 0.48614063292493953 + ], + [ + -0.6009028689199978, + 0.0, + -0.11476223599505815 + ], + [ + 0.48614063292493953, + -0.3532018444114118, + -0.11476223599505815 + ], + [ + 0.48614063292493953, + 0.3532018444114118, + -0.11476223599505815 + ], + [ + -0.18568919846494072, + -0.5714925891468163, + -0.11476223599505815 + ], + [ + -0.18568919846494072, + 0.5714925891468163, + -0.11476223599505815 + ], + [ + 0.6009028689199978, + 0.0, + 0.11476223599505815 + ], + [ + 0.1856891984649407, + -0.5714925891468163, + 0.11476223599505815 + ], + [ + 0.1856891984649407, + 0.5714925891468163, + 0.11476223599505815 + ], + [ + -0.48614063292493953, + -0.3532018444114118, + 0.11476223599505815 + ], + [ + -0.48614063292493953, + 0.3532018444114118, + 0.11476223599505815 + ], + [ + 0.5178601348289863, + -0.37624741151184876, + 0.32005516474291673 + ], + [ + 0.5178601348289863, + 0.3762474115118488, + 0.32005516474291673 + ], + [ + -0.6401103294858336, + 0.0, + 0.32005516474291673 + ], + [ + -0.19780497008606956, + -0.6087811000053397, + 0.32005516474291673 + ], + [ + -0.19780497008606956, + 0.6087811000053397, + 0.32005516474291673 + ], + [ + 0.6401103294858335, + 0.0, + -0.3200551647429168 + ], + [ + -0.5178601348289863, + -0.37624741151184876, + -0.3200551647429168 + ], + [ + -0.5178601348289863, + 0.3762474115118488, + -0.3200551647429168 + ], + [ + 0.19780497008606956, + -0.6087811000053397, + -0.3200551647429168 + ], + [ + 0.19780497008606956, + 0.6087811000053397, + -0.3200551647429168 + ] + ], + "symmetry_group": "[5,3]", + "short_code": "C07" + }, + "Triakis Tetrahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + 0.0, + -1.0267866534130576 + ], + [ + 0.0, + 0.0, + 0.6160719920478345 + ], + [ + -0.9680637406136193, + 0.0, + 0.34226221780435256 + ], + [ + -0.2904191221840858, + -0.5030206751123901, + -0.20535733068261156 + ], + [ + -0.2904191221840858, + 0.5030206751123901, + -0.20535733068261156 + ], + [ + 0.48403187030680966, + -0.8383677918539836, + 0.34226221780435256 + ], + [ + 0.48403187030680966, + 0.8383677918539836, + 0.34226221780435256 + ], + [ + 0.5808382443681716, + 0.0, + -0.20535733068261156 + ] + ], + "symmetry_group": "[3,3]", + "short_code": "C03" + } +} diff --git a/coxeter/families/data/johnson.json b/coxeter/families/data/johnson.json new file mode 100644 index 00000000..744f6039 --- /dev/null +++ b/coxeter/families/data/johnson.json @@ -0,0 +1,11974 @@ +{ + "Augmented Dodecahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + 0.0, + 0.7016651165653368 + ], + [ + 0.0, + 0.0, + -0.7016651165653369 + ], + [ + 0.0893374086026006, + -0.6554761571436897, + 0.23388837218844566 + ], + [ + 0.0893374086026006, + 0.6554761571436897, + 0.23388837218844566 + ], + [ + 0.23388837218844566, + -0.4051065439299674, + -0.5229902993601356 + ], + [ + 0.23388837218844566, + 0.4051065439299674, + -0.5229902993601356 + ], + [ + 0.5229902993601356, + -0.4051065439299674, + 0.23388837218844566 + ], + [ + 0.5229902993601356, + 0.4051065439299674, + 0.23388837218844566 + ], + [ + -0.6123277079627363, + -0.25036961321372225, + 0.23388837218844566 + ], + [ + -0.6123277079627363, + 0.25036961321372225, + 0.23388837218844566 + ], + [ + 0.6123277079627363, + -0.25036961321372225, + -0.23388837218844563 + ], + [ + 0.6123277079627363, + 0.25036961321372225, + -0.23388837218844563 + ], + [ + -0.46777674437689126, + 0.0, + -0.5229902993601356 + ], + [ + -0.23388837218844563, + -0.4051065439299674, + 0.5229902993601356 + ], + [ + -0.23388837218844563, + 0.4051065439299674, + 0.5229902993601356 + ], + [ + 0.4677767443768913, + 0.0, + 0.5229902993601356 + ], + [ + -0.5229902993601356, + -0.4051065439299674, + -0.23388837218844563 + ], + [ + -0.5229902993601356, + 0.4051065439299674, + -0.23388837218844563 + ], + [ + -0.4982980469157443, + 0.0, + 0.6522806116765543 + ], + [ + -0.0893374086026006, + -0.6554761571436897, + -0.23388837218844563 + ], + [ + -0.0893374086026006, + 0.6554761571436897, + -0.23388837218844563 + ] + ], + "short_name": "J58" + }, + "Augmented Hexagonal Prism": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.7066613972587069, + 0.0, + -0.35333069862935346 + ], + [ + -0.7066613972587069, + 0.0, + 0.35333069862935346 + ], + [ + -0.35333069862935346, + -0.6119867218998473, + -0.35333069862935346 + ], + [ + -0.35333069862935346, + -0.6119867218998473, + 0.35333069862935346 + ], + [ + -0.35333069862935346, + 0.6119867218998473, + -0.35333069862935346 + ], + [ + -0.35333069862935346, + 0.6119867218998473, + 0.35333069862935346 + ], + [ + 0.35333069862935346, + -0.6119867218998473, + -0.35333069862935346 + ], + [ + 0.35333069862935346, + -0.6119867218998473, + 0.35333069862935346 + ], + [ + 0.35333069862935346, + 0.6119867218998473, + -0.35333069862935346 + ], + [ + 0.35333069862935346, + 0.6119867218998473, + 0.35333069862935346 + ], + [ + 0.7066613972587069, + 0.0, + -0.35333069862935346 + ], + [ + 0.7066613972587069, + 0.0, + 0.35333069862935346 + ], + [ + 0.9627360089955379, + 0.5558358939521197, + 0.0 + ] + ], + "short_name": "J54" + }, + "Augmented Pentagonal Prism": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.6801662411235555, + 0.0, + -0.3997916856396322 + ], + [ + 0.6801662411235555, + 0.0, + 0.3997916856396322 + ], + [ + 0.21018292750730688, + -0.6468765357845382, + -0.3997916856396322 + ], + [ + 0.21018292750730688, + -0.6468765357845382, + 0.3997916856396322 + ], + [ + 0.21018292750730688, + 0.6468765357845382, + -0.3997916856396322 + ], + [ + 0.21018292750730688, + 0.6468765357845382, + 0.3997916856396322 + ], + [ + -0.5502660480690846, + -0.3997916856396322, + -0.3997916856396322 + ], + [ + -0.5502660480690846, + -0.3997916856396322, + 0.3997916856396322 + ], + [ + -0.5502660480690846, + 0.3997916856396322, + -0.3997916856396322 + ], + [ + -0.5502660480690846, + 0.3997916856396322, + 0.3997916856396322 + ], + [ + 0.9025853693591405, + 0.6557666559948423, + 0.0 + ] + ], + "short_name": "J52" + }, + "Augmented Sphenocorona": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.4148300092035722, + 0.0 + ], + [ + 0.0, + 0.4148300092035722, + 0.0 + ], + [ + -0.7074734510982262, + 0.4148300092035722, + 0.4333786590667668 + ], + [ + -0.4148300092035722, + 0.0, + 1.089588705868519 + ], + [ + -0.7074734510982262, + -0.4148300092035722, + 0.4333786590667668 + ], + [ + 0.7074734510982262, + 0.4148300092035722, + 0.4333786590667668 + ], + [ + 0.4148300092035722, + 0.0, + 1.089588705868519 + ], + [ + 0.7074734510982262, + -0.4148300092035722, + 0.4333786590667668 + ], + [ + 0.0, + 0.6549565392665672, + 0.794150486811693 + ], + [ + 0.0, + -0.6549565392665672, + 0.794150486811693 + ], + [ + 0.6601817141967568, + 0.0, + -0.28356994524762164 + ] + ], + "short_name": "J87" + }, + "Augmented Triangular Prism": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.3301127993994366, + -0.5717721407886169, + -0.5717721407886169 + ], + [ + -0.3301127993994366, + -0.5717721407886169, + 0.5717721407886169 + ], + [ + -0.3301127993994366, + 0.5717721407886169, + -0.5717721407886169 + ], + [ + -0.3301127993994366, + 0.5717721407886169, + 0.5717721407886169 + ], + [ + 0.6602255987988732, + 0.0, + -0.5717721407886169 + ], + [ + 0.6602255987988732, + 0.0, + 0.5717721407886169 + ], + [ + 0.5693603577448987, + 0.9861610674297566, + 0.0 + ] + ], + "short_name": "J49" + }, + "Augmented Tridiminished Icosahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + 0.0, + -1.4071113862985793 + ], + [ + -0.5167066676788791, + 0.0, + -0.676377809098501 + ], + [ + -0.25835333383943954, + -0.4474811005147129, + 0.676377809098501 + ], + [ + -0.25835333383943954, + 0.4474811005147129, + 0.676377809098501 + ], + [ + 0.25835333383943954, + -0.4474811005147129, + -0.676377809098501 + ], + [ + 0.25835333383943954, + 0.4474811005147129, + -0.676377809098501 + ], + [ + 0.5167066676788791, + 0.0, + 0.676377809098501 + ], + [ + -0.8360489505181229, + 0.0, + 0.15967114141962196 + ], + [ + 0.4180244752590615, + -0.7240396299560136, + 0.15967114141962196 + ], + [ + 0.4180244752590615, + 0.7240396299560136, + 0.15967114141962196 + ] + ], + "short_name": "J64" + }, + "Augmented Truncated Cube": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.20035336303449186, + 0.48369580630493053, + -0.48369580630493053 + ], + [ + -0.20035336303449186, + 0.48369580630493053, + 0.48369580630493053 + ], + [ + -0.20035336303449186, + -0.48369580630493053, + -0.48369580630493053 + ], + [ + -0.20035336303449186, + -0.48369580630493053, + 0.48369580630493053 + ], + [ + 0.0, + -0.28334244327043867, + 0.7670382495753694 + ], + [ + 0.0, + 0.28334244327043867, + 0.7670382495753694 + ], + [ + 0.20035336303449186, + 0.48369580630493053, + -0.48369580630493053 + ], + [ + 0.20035336303449186, + 0.48369580630493053, + 0.48369580630493053 + ], + [ + 0.20035336303449186, + -0.48369580630493053, + -0.48369580630493053 + ], + [ + 0.20035336303449186, + -0.48369580630493053, + 0.48369580630493053 + ], + [ + -0.28334244327043867, + 0.0, + 0.7670382495753694 + ], + [ + 0.28334244327043867, + 0.0, + 0.7670382495753694 + ], + [ + 0.48369580630493053, + -0.20035336303449186, + -0.48369580630493053 + ], + [ + 0.48369580630493053, + -0.20035336303449186, + 0.48369580630493053 + ], + [ + 0.48369580630493053, + 0.20035336303449186, + -0.48369580630493053 + ], + [ + 0.48369580630493053, + 0.20035336303449186, + 0.48369580630493053 + ], + [ + 0.48369580630493053, + 0.48369580630493053, + -0.20035336303449186 + ], + [ + 0.48369580630493053, + 0.48369580630493053, + 0.20035336303449186 + ], + [ + 0.48369580630493053, + -0.48369580630493053, + -0.20035336303449186 + ], + [ + 0.48369580630493053, + -0.48369580630493053, + 0.20035336303449186 + ], + [ + -0.48369580630493053, + -0.20035336303449186, + -0.48369580630493053 + ], + [ + -0.48369580630493053, + -0.20035336303449186, + 0.48369580630493053 + ], + [ + -0.48369580630493053, + 0.20035336303449186, + -0.48369580630493053 + ], + [ + -0.48369580630493053, + 0.20035336303449186, + 0.48369580630493053 + ], + [ + -0.48369580630493053, + 0.48369580630493053, + -0.20035336303449186 + ], + [ + -0.48369580630493053, + 0.48369580630493053, + 0.20035336303449186 + ], + [ + -0.48369580630493053, + -0.48369580630493053, + -0.20035336303449186 + ], + [ + -0.48369580630493053, + -0.48369580630493053, + 0.20035336303449186 + ] + ], + "short_name": "J66" + }, + "Augmented Truncated Dodecahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.3646508953615872, + 0.5611400287352863 + ], + [ + 0.0, + -0.3646508953615872, + -0.5611400287352863 + ], + [ + 0.0, + 0.3646508953615872, + 0.5611400287352863 + ], + [ + 0.0, + 0.3646508953615872, + -0.5611400287352863 + ], + [ + 0.09585416037684251, + -0.6596596667231519, + 0.05924112907597211 + ], + [ + 0.09585416037684251, + 0.6596596667231519, + 0.05924112907597211 + ], + [ + 0.15509528945281462, + -0.4773342190423583, + 0.4426577705833422 + ], + [ + 0.15509528945281462, + 0.4773342190423583, + 0.4426577705833422 + ], + [ + -0.6203811578112585, + 0.0, + -0.2509494498296571 + ], + [ + -0.46528586835844393, + -0.4773342190423583, + 0.05924112907597211 + ], + [ + -0.46528586835844393, + 0.4773342190423583, + 0.05924112907597211 + ], + [ + -0.31019057890562923, + -0.5900175427231295, + -0.05924112907597211 + ], + [ + -0.31019057890562923, + 0.5900175427231295, + -0.05924112907597211 + ], + [ + -0.15509528945281462, + -0.4773342190423583, + -0.4426577705833422 + ], + [ + -0.15509528945281462, + 0.4773342190423583, + -0.4426577705833422 + ], + [ + 0.31019057890562923, + -0.5900175427231295, + 0.05924112907597211 + ], + [ + 0.31019057890562923, + 0.5900175427231295, + 0.05924112907597211 + ], + [ + 0.6203811578112585, + 0.0, + 0.2509494498296571 + ], + [ + 0.40604473928247176, + -0.2950087713615647, + -0.4426577705833422 + ], + [ + 0.40604473928247176, + 0.2950087713615647, + -0.4426577705833422 + ], + [ + 0.46528586835844393, + -0.4773342190423583, + -0.05924112907597211 + ], + [ + 0.46528586835844393, + 0.4773342190423583, + -0.05924112907597211 + ], + [ + 0.5018988996593142, + 0.0, + 0.4426577705833422 + ], + [ + 0.5018988996593142, + -0.3646508953615872, + -0.2509494498296571 + ], + [ + 0.5018988996593142, + 0.3646508953615872, + -0.2509494498296571 + ], + [ + -0.5977530600361568, + -0.2950087713615647, + 0.05924112907597211 + ], + [ + -0.5977530600361568, + 0.2950087713615647, + 0.05924112907597211 + ], + [ + 0.5977530600361568, + -0.2950087713615647, + -0.05924112907597211 + ], + [ + 0.5977530600361568, + 0.2950087713615647, + -0.05924112907597211 + ], + [ + 0.6569941891121288, + -0.11268332368077112, + 0.05924112907597211 + ], + [ + 0.6569941891121288, + 0.11268332368077112, + 0.05924112907597211 + ], + [ + -0.6569941891121288, + -0.11268332368077112, + -0.05924112907597211 + ], + [ + -0.6569941891121288, + 0.11268332368077112, + -0.05924112907597211 + ], + [ + 0.2143364185287867, + -0.2950087713615647, + 0.5611400287352863 + ], + [ + 0.2143364185287867, + -0.2950087713615647, + -0.5611400287352863 + ], + [ + 0.2143364185287867, + 0.2950087713615647, + 0.5611400287352863 + ], + [ + 0.2143364185287867, + 0.2950087713615647, + -0.5611400287352863 + ], + [ + 0.19170832075368505, + -0.5900175427231295, + 0.2509494498296571 + ], + [ + 0.19170832075368505, + 0.5900175427231295, + 0.2509494498296571 + ], + [ + -0.2143364185287867, + -0.2950087713615647, + 0.5611400287352863 + ], + [ + -0.2143364185287867, + -0.2950087713615647, + -0.5611400287352863 + ], + [ + -0.2143364185287867, + 0.2950087713615647, + 0.5611400287352863 + ], + [ + -0.2143364185287867, + 0.2950087713615647, + -0.5611400287352863 + ], + [ + -0.3468036102064997, + -0.11268332368077112, + 0.5611400287352863 + ], + [ + -0.3468036102064997, + -0.11268332368077112, + -0.5611400287352863 + ], + [ + -0.3468036102064997, + 0.11268332368077112, + 0.5611400287352863 + ], + [ + -0.3468036102064997, + 0.11268332368077112, + -0.5611400287352863 + ], + [ + 0.3468036102064997, + -0.11268332368077112, + 0.5611400287352863 + ], + [ + 0.3468036102064997, + -0.11268332368077112, + -0.5611400287352863 + ], + [ + 0.3468036102064997, + 0.11268332368077112, + 0.5611400287352863 + ], + [ + 0.3468036102064997, + 0.11268332368077112, + -0.5611400287352863 + ], + [ + -0.5018988996593142, + 0.0, + -0.4426577705833422 + ], + [ + -0.5018988996593142, + -0.3646508953615872, + 0.2509494498296571 + ], + [ + -0.5018988996593142, + 0.3646508953615872, + 0.2509494498296571 + ], + [ + -0.19170832075368505, + -0.5900175427231295, + -0.2509494498296571 + ], + [ + -0.19170832075368505, + 0.5900175427231295, + -0.2509494498296571 + ], + [ + -0.40604473928247176, + -0.2950087713615647, + 0.4426577705833422 + ], + [ + -0.40604473928247176, + 0.2950087713615647, + 0.4426577705833422 + ], + [ + -0.09585416037684252, + -0.6596596667231519, + -0.05924112907597211 + ], + [ + -0.09585416037684252, + 0.6596596667231519, + -0.05924112907597211 + ], + [ + -0.05924112907597211, + 0.1823254476807936, + 0.6796222868872306 + ], + [ + -0.19170832075368505, + 0.0, + 0.6796222868872306 + ], + [ + -0.05924112907597211, + -0.1823254476807936, + 0.6796222868872306 + ], + [ + 0.15509528945281462, + -0.11268332368077112, + 0.6796222868872306 + ], + [ + 0.15509528945281462, + 0.11268332368077112, + 0.6796222868872306 + ] + ], + "short_name": "J68" + }, + "Augmented Truncated Tetrahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.6358930857205072, + -0.3894033977447816 + ], + [ + 0.0, + 0.6358930857205072, + -0.3894033977447816 + ], + [ + -0.3671330442165566, + -0.6358930857205072, + 0.1298011325815939 + ], + [ + -0.3671330442165566, + 0.6358930857205072, + 0.1298011325815939 + ], + [ + -0.1835665221082783, + -0.3179465428602536, + 0.6490056629079695 + ], + [ + -0.1835665221082783, + 0.3179465428602536, + 0.6490056629079695 + ], + [ + 0.1835665221082783, + -0.3179465428602536, + -0.9086079280711573 + ], + [ + 0.3671330442165566, + 0.0, + 0.6490056629079695 + ], + [ + 0.7342660884331133, + 0.0, + 0.1298011325815939 + ], + [ + -0.5506995663248349, + -0.3179465428602536, + -0.3894033977447816 + ], + [ + -0.5506995663248349, + 0.3179465428602536, + -0.3894033977447816 + ], + [ + 0.5506995663248349, + -0.3179465428602536, + -0.3894033977447816 + ], + [ + 0.5506995663248349, + 0.3179465428602536, + -0.3894033977447816 + ], + [ + -0.3671330442165566, + 0.0, + -0.9086079280711573 + ], + [ + 0.1835665221082783, + 0.3179465428602536, + -0.9086079280711573 + ] + ], + "short_name": "J65" + }, + "Biaugmented Pentagonal Prism": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.6548556830820478, + 0.0, + -0.3849145128955413 + ], + [ + 0.6548556830820478, + 0.0, + 0.3849145128955413 + ], + [ + 0.20236153493536752, + -0.6228047646280955, + -0.3849145128955413 + ], + [ + 0.20236153493536752, + -0.6228047646280955, + 0.3849145128955413 + ], + [ + 0.20236153493536752, + 0.6228047646280955, + -0.3849145128955413 + ], + [ + 0.20236153493536752, + 0.6228047646280955, + 0.3849145128955413 + ], + [ + -0.5297893764763915, + -0.3849145128955413, + -0.3849145128955413 + ], + [ + -0.5297893764763915, + -0.3849145128955413, + 0.3849145128955413 + ], + [ + -0.5297893764763915, + 0.3849145128955413, + -0.3849145128955413 + ], + [ + -0.5297893764763915, + 0.3849145128955413, + 0.3849145128955413 + ], + [ + -1.0741407009674995, + 0.0, + 0.0 + ], + [ + 0.8689980814325257, + 0.6313640629157956, + 0.0 + ] + ], + "short_name": "J53" + }, + "Biaugmented Triangular Prism": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.29850602571231477, + -0.5170276028991908, + -0.5170276028991908 + ], + [ + -0.29850602571231477, + -0.5170276028991908, + 0.5170276028991908 + ], + [ + -0.29850602571231477, + 0.5170276028991908, + -0.5170276028991908 + ], + [ + -0.29850602571231477, + 0.5170276028991908, + 0.5170276028991908 + ], + [ + 0.5970120514246295, + 0.0, + -0.5170276028991908 + ], + [ + 0.5970120514246295, + 0.0, + 0.5170276028991908 + ], + [ + -1.0296934738536014, + 0.0, + 0.0 + ], + [ + 0.5148467369268007, + 0.8917407064682664, + 0.0 + ] + ], + "short_name": "J50" + }, + "Biaugmented Truncated Cube": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.1926397011640934, + 0.4650733792018544, + 0.4650733792018544 + ], + [ + -0.1926397011640934, + 0.4650733792018544, + -0.4650733792018544 + ], + [ + -0.1926397011640934, + -0.4650733792018544, + 0.4650733792018544 + ], + [ + -0.1926397011640934, + -0.4650733792018544, + -0.4650733792018544 + ], + [ + 0.0, + -0.272433678037761, + 0.7375070572396154 + ], + [ + 0.0, + -0.272433678037761, + -0.7375070572396154 + ], + [ + 0.0, + 0.272433678037761, + 0.7375070572396154 + ], + [ + 0.0, + 0.272433678037761, + -0.7375070572396154 + ], + [ + 0.1926397011640934, + 0.4650733792018544, + 0.4650733792018544 + ], + [ + 0.1926397011640934, + 0.4650733792018544, + -0.4650733792018544 + ], + [ + 0.1926397011640934, + -0.4650733792018544, + 0.4650733792018544 + ], + [ + 0.1926397011640934, + -0.4650733792018544, + -0.4650733792018544 + ], + [ + -0.272433678037761, + 0.0, + 0.7375070572396154 + ], + [ + -0.272433678037761, + 0.0, + -0.7375070572396154 + ], + [ + 0.272433678037761, + 0.0, + 0.7375070572396154 + ], + [ + 0.272433678037761, + 0.0, + -0.7375070572396154 + ], + [ + 0.4650733792018544, + -0.1926397011640934, + 0.4650733792018544 + ], + [ + 0.4650733792018544, + -0.1926397011640934, + -0.4650733792018544 + ], + [ + 0.4650733792018544, + 0.1926397011640934, + 0.4650733792018544 + ], + [ + 0.4650733792018544, + 0.1926397011640934, + -0.4650733792018544 + ], + [ + 0.4650733792018544, + 0.4650733792018544, + -0.1926397011640934 + ], + [ + 0.4650733792018544, + 0.4650733792018544, + 0.1926397011640934 + ], + [ + 0.4650733792018544, + -0.4650733792018544, + -0.1926397011640934 + ], + [ + 0.4650733792018544, + -0.4650733792018544, + 0.1926397011640934 + ], + [ + -0.4650733792018544, + -0.1926397011640934, + 0.4650733792018544 + ], + [ + -0.4650733792018544, + -0.1926397011640934, + -0.4650733792018544 + ], + [ + -0.4650733792018544, + 0.1926397011640934, + 0.4650733792018544 + ], + [ + -0.4650733792018544, + 0.1926397011640934, + -0.4650733792018544 + ], + [ + -0.4650733792018544, + 0.4650733792018544, + -0.1926397011640934 + ], + [ + -0.4650733792018544, + 0.4650733792018544, + 0.1926397011640934 + ], + [ + -0.4650733792018544, + -0.4650733792018544, + -0.1926397011640934 + ], + [ + -0.4650733792018544, + -0.4650733792018544, + 0.1926397011640934 + ] + ], + "short_name": "J67" + }, + "Bigyrate Diminished Rhombicosidodecahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.147074693143019, + -0.20243094860089703, + 0.6072928458026912 + ], + [ + 0.47594370478073167, + 0.0, + -0.4526493618213717 + ], + [ + -0.23797185239036583, + 0.07732174199065969, + 0.6072928458026912 + ], + [ + 0.38504654553338485, + 0.2797526905915567, + -0.4526493618213717 + ], + [ + 0.23797185239036583, + -0.577758568431609, + 0.20243094860089703 + ], + [ + 0.38504654553338485, + -0.5299711038120314, + -0.04778746461957764 + ], + [ + -0.147074693143019, + 0.6072928458026912, + 0.20243094860089703 + ], + [ + 0.0, + 0.6550803104222687, + -0.04778746461957764 + ], + [ + -0.147074693143019, + -0.4526493618213717, + 0.4526493618213717 + ], + [ + 0.38504654553338485, + -0.2797526905915567, + -0.4526493618213717 + ], + [ + -0.38504654553338485, + 0.2797526905915567, + 0.4526493618213717 + ], + [ + 0.147074693143019, + 0.4526493618213717, + -0.4526493618213717 + ], + [ + -0.4101699024531891, + -0.13327228010897105, + 0.49539176956606845 + ], + [ + -0.5572445955962081, + 0.06915866849192599, + 0.340748285584749 + ], + [ + 0.0, + -0.6550803104222687, + 0.04778746461957764 + ], + [ + 0.147074693143019, + -0.6072928458026912, + -0.20243094860089703 + ], + [ + -0.38504654553338485, + 0.5299711038120314, + 0.04778746461957764 + ], + [ + -0.23797185239036583, + 0.577758568431609, + -0.20243094860089703 + ], + [ + 0.23797185239036583, + 0.07732174199065969, + 0.6072928458026912 + ], + [ + 0.6230183979237507, + 0.20243094860089703, + -0.04778746461957764 + ], + [ + 0.147074693143019, + -0.4526493618213717, + 0.4526493618213717 + ], + [ + 0.5321212386764038, + -0.32754015521113433, + -0.20243094860089703 + ], + [ + -0.147074693143019, + 0.4526493618213717, + 0.4526493618213717 + ], + [ + 0.23797185239036583, + 0.577758568431609, + -0.20243094860089703 + ], + [ + 0.4101699024531891, + -0.3834906933294457, + 0.340748285584749 + ], + [ + 0.648141754843555, + -0.05595053811831134, + 0.09052987236427434 + ], + [ + 0.147074693143019, + 0.4526493618213717, + 0.4526493618213717 + ], + [ + 0.38504654553338485, + 0.5299711038120314, + 0.04778746461957764 + ], + [ + 0.4101699024531891, + -0.13327228010897105, + 0.49539176956606845 + ], + [ + 0.5572445955962081, + 0.06915866849192599, + 0.340748285584749 + ], + [ + 0.38504654553338485, + 0.2797526905915567, + 0.4526493618213717 + ], + [ + 0.5321212386764038, + 0.32754015521113433, + 0.20243094860089703 + ], + [ + 0.5572445955962081, + -0.335703228709868, + 0.09052987236427434 + ], + [ + 0.147074693143019, + -0.20243094860089703, + 0.6072928458026912 + ], + [ + 0.6230183979237507, + -0.04778746461957764, + -0.20243094860089703 + ], + [ + 0.0, + 0.25021841322047467, + 0.6072928458026912 + ], + [ + 0.47594370478073167, + 0.40486189720179405, + -0.20243094860089703 + ], + [ + 0.147074693143019, + 0.6072928458026912, + 0.20243094860089703 + ], + [ + -0.23797185239036583, + -0.577758568431609, + 0.20243094860089703 + ], + [ + 0.147074693143019, + -0.4526493618213717, + -0.4526493618213717 + ], + [ + -0.5321212386764038, + 0.32754015521113433, + 0.20243094860089703 + ], + [ + -0.147074693143019, + 0.4526493618213717, + -0.4526493618213717 + ], + [ + -0.3850465455333849, + -0.5299711038120314, + -0.04778746461957764 + ], + [ + -0.147074693143019, + -0.4526493618213717, + -0.4526493618213717 + ], + [ + -0.6230183979237507, + 0.20243094860089703, + -0.04778746461957764 + ], + [ + -0.38504654553338485, + 0.2797526905915567, + -0.4526493618213717 + ], + [ + -0.5321212386764038, + -0.32754015521113433, + -0.20243094860089703 + ], + [ + -0.38504654553338485, + -0.2797526905915567, + -0.4526493618213717 + ], + [ + -0.6230183979237507, + -0.04778746461957764, + -0.20243094860089703 + ], + [ + -0.47594370478073167, + 0.0, + -0.4526493618213717 + ], + [ + -0.147074693143019, + -0.6072928458026912, + -0.20243094860089703 + ], + [ + -0.4101699024531891, + -0.3834906933294457, + 0.340748285584749 + ], + [ + -0.648141754843555, + -0.05595053811831134, + 0.09052987236427434 + ], + [ + -0.47594370478073167, + 0.40486189720179405, + -0.20243094860089703 + ], + [ + -0.5572445955962081, + -0.335703228709868, + 0.09052987236427434 + ] + ], + "short_name": "J79" + }, + "Bilunabirotunda": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.8983627305605315, + 0.0, + -0.34314402884795914 + ], + [ + -0.8983627305605315, + 0.0, + 0.34314402884795914 + ], + [ + -0.34314402884795914, + -0.34314402884795914, + -0.5552187017125724 + ], + [ + -0.34314402884795914, + -0.34314402884795914, + 0.5552187017125724 + ], + [ + -0.34314402884795914, + 0.34314402884795914, + -0.5552187017125724 + ], + [ + -0.34314402884795914, + 0.34314402884795914, + 0.5552187017125724 + ], + [ + 0.0, + -0.5552187017125724, + 0.0 + ], + [ + 0.0, + 0.5552187017125724, + 0.0 + ], + [ + 0.34314402884795914, + -0.34314402884795914, + -0.5552187017125724 + ], + [ + 0.34314402884795914, + -0.34314402884795914, + 0.5552187017125724 + ], + [ + 0.34314402884795914, + 0.34314402884795914, + -0.5552187017125724 + ], + [ + 0.34314402884795914, + 0.34314402884795914, + 0.5552187017125724 + ], + [ + 0.8983627305605315, + 0.0, + -0.34314402884795914 + ], + [ + 0.8983627305605315, + 0.0, + 0.34314402884795914 + ] + ], + "short_name": "J91" + }, + "Diminished Rhombicosidodecahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.147074693143019, + -0.20243094860089703, + 0.6072928458026912 + ], + [ + 0.47594370478073167, + 0.0, + -0.4526493618213717 + ], + [ + -0.23797185239036583, + 0.07732174199065969, + 0.6072928458026912 + ], + [ + 0.38504654553338485, + 0.2797526905915567, + -0.4526493618213717 + ], + [ + 0.23797185239036583, + -0.577758568431609, + 0.20243094860089703 + ], + [ + 0.38504654553338485, + -0.5299711038120314, + -0.04778746461957764 + ], + [ + -0.147074693143019, + 0.6072928458026912, + 0.20243094860089703 + ], + [ + 0.0, + 0.6550803104222687, + -0.04778746461957764 + ], + [ + -0.147074693143019, + -0.4526493618213717, + 0.4526493618213717 + ], + [ + 0.38504654553338485, + -0.2797526905915567, + -0.4526493618213717 + ], + [ + -0.38504654553338485, + 0.2797526905915567, + 0.4526493618213717 + ], + [ + 0.147074693143019, + 0.4526493618213717, + -0.4526493618213717 + ], + [ + -0.38504654553338485, + -0.2797526905915567, + 0.4526493618213717 + ], + [ + -0.47594370478073167, + 0.0, + 0.4526493618213717 + ], + [ + 0.0, + -0.6550803104222687, + 0.04778746461957764 + ], + [ + 0.147074693143019, + -0.6072928458026912, + -0.20243094860089703 + ], + [ + -0.38504654553338485, + 0.5299711038120314, + 0.04778746461957764 + ], + [ + -0.23797185239036583, + 0.577758568431609, + -0.20243094860089703 + ], + [ + 0.23797185239036583, + 0.07732174199065969, + 0.6072928458026912 + ], + [ + 0.6230183979237507, + 0.20243094860089703, + -0.04778746461957764 + ], + [ + 0.147074693143019, + -0.4526493618213717, + 0.4526493618213717 + ], + [ + 0.5321212386764038, + -0.32754015521113433, + -0.20243094860089703 + ], + [ + -0.147074693143019, + 0.4526493618213717, + 0.4526493618213717 + ], + [ + 0.23797185239036583, + 0.577758568431609, + -0.20243094860089703 + ], + [ + 0.38504654553338485, + -0.2797526905915567, + 0.4526493618213717 + ], + [ + 0.6230183979237507, + -0.20243094860089703, + 0.04778746461957764 + ], + [ + 0.147074693143019, + 0.4526493618213717, + 0.4526493618213717 + ], + [ + 0.38504654553338485, + 0.5299711038120314, + 0.04778746461957764 + ], + [ + 0.47594370478073167, + 0.0, + 0.4526493618213717 + ], + [ + 0.6230183979237507, + 0.04778746461957764, + 0.20243094860089703 + ], + [ + 0.38504654553338485, + 0.2797526905915567, + 0.4526493618213717 + ], + [ + 0.5321212386764038, + 0.32754015521113433, + 0.20243094860089703 + ], + [ + 0.47594370478073167, + -0.40486189720179405, + 0.20243094860089703 + ], + [ + 0.147074693143019, + -0.20243094860089703, + 0.6072928458026912 + ], + [ + 0.6230183979237507, + -0.04778746461957764, + -0.20243094860089703 + ], + [ + 0.0, + 0.25021841322047467, + 0.6072928458026912 + ], + [ + 0.47594370478073167, + 0.40486189720179405, + -0.20243094860089703 + ], + [ + 0.147074693143019, + 0.6072928458026912, + 0.20243094860089703 + ], + [ + -0.23797185239036583, + -0.577758568431609, + 0.20243094860089703 + ], + [ + 0.147074693143019, + -0.4526493618213717, + -0.4526493618213717 + ], + [ + -0.5321212386764038, + 0.32754015521113433, + 0.20243094860089703 + ], + [ + -0.147074693143019, + 0.4526493618213717, + -0.4526493618213717 + ], + [ + -0.3850465455333849, + -0.5299711038120314, + -0.04778746461957764 + ], + [ + -0.147074693143019, + -0.4526493618213717, + -0.4526493618213717 + ], + [ + -0.6230183979237507, + 0.20243094860089703, + -0.04778746461957764 + ], + [ + -0.38504654553338485, + 0.2797526905915567, + -0.4526493618213717 + ], + [ + -0.5321212386764038, + -0.32754015521113433, + -0.20243094860089703 + ], + [ + -0.38504654553338485, + -0.2797526905915567, + -0.4526493618213717 + ], + [ + -0.6230183979237507, + -0.04778746461957764, + -0.20243094860089703 + ], + [ + -0.47594370478073167, + 0.0, + -0.4526493618213717 + ], + [ + -0.147074693143019, + -0.6072928458026912, + -0.20243094860089703 + ], + [ + -0.47594370478073167, + -0.40486189720179405, + 0.20243094860089703 + ], + [ + -0.6230183979237507, + 0.04778746461957764, + 0.20243094860089703 + ], + [ + -0.47594370478073167, + 0.40486189720179405, + -0.20243094860089703 + ], + [ + -0.6230183979237507, + -0.20243094860089703, + 0.04778746461957764 + ] + ], + "short_name": "J76" + }, + "Triangular Dipyramid": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + 0.0, + -1.3218021521667291 + ], + [ + 0.0, + 0.0, + 1.3218021521667291 + ], + [ + -0.4673276325920336, + -0.8094352034302832, + 0.0 + ], + [ + -0.4673276325920336, + 0.8094352034302832, + 0.0 + ], + [ + 0.9346552651840672, + 0.0, + 0.0 + ] + ], + "short_name": "J12" + }, + "Pentagonal Dipyramid": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + 0.0, + -0.6222857864688324 + ], + [ + 0.0, + 0.0, + 0.6222857864688324 + ], + [ + 1.00687955322253, + 0.0, + 0.0 + ], + [ + 0.3111428932344162, + -0.9575993602166403, + 0.0 + ], + [ + 0.3111428932344162, + 0.9575993602166403, + 0.0 + ], + [ + -0.8145826698456813, + -0.5918289522190375, + 0.0 + ], + [ + -0.8145826698456813, + 0.5918289522190375, + 0.0 + ] + ], + "short_name": "J13" + }, + "Disphenocingulum": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.3210428066822091, + 0.0, + 0.7091437134633302 + ], + [ + -0.3210428066822091, + -0.4925638518530002, + 0.2972519962155847 + ], + [ + -0.3210428066822091, + 0.4925638518530002, + 0.2972519962155847 + ], + [ + 0.0, + -0.3210428066822091, + -0.7091437134633302 + ], + [ + 0.0, + 0.3210428066822091, + -0.7091437134633302 + ], + [ + 0.0, + -0.7232986224368867, + -0.20867973515809793 + ], + [ + 0.0, + 0.7232986224368867, + -0.20867973515809793 + ], + [ + 0.3210428066822091, + 0.0, + 0.7091437134633302 + ], + [ + 0.3210428066822091, + -0.4925638518530002, + 0.2972519962155847 + ], + [ + 0.3210428066822091, + 0.4925638518530002, + 0.2972519962155847 + ], + [ + -0.4925638518530002, + -0.3210428066822091, + -0.2972519962155847 + ], + [ + -0.4925638518530002, + 0.3210428066822091, + -0.2972519962155847 + ], + [ + 0.4925638518530002, + -0.3210428066822091, + -0.2972519962155847 + ], + [ + 0.4925638518530002, + 0.3210428066822091, + -0.2972519962155847 + ], + [ + -0.7232986224368867, + 0.0, + 0.20867973515809793 + ], + [ + 0.7232986224368867, + 0.0, + 0.20867973515809793 + ] + ], + "short_name": "J90" + }, + "Elongated Pentagonal Cupola": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.7505684271625788, + -0.46387679886902344 + ], + [ + 0.0, + -0.7505684271625788, + 0.0 + ], + [ + 0.0, + 0.7505684271625788, + -0.46387679886902344 + ], + [ + 0.0, + 0.7505684271625788, + 0.0 + ], + [ + 0.3945971739336914, + 0.0, + 0.24387446535567534 + ], + [ + 0.12193723267783767, + -0.3752842135812894, + 0.24387446535567534 + ], + [ + 0.12193723267783767, + 0.3752842135812894, + 0.24387446535567534 + ], + [ + -0.4411730523225211, + -0.607222613015801, + -0.46387679886902344 + ], + [ + -0.4411730523225211, + -0.607222613015801, + 0.0 + ], + [ + -0.4411730523225211, + 0.607222613015801, + -0.46387679886902344 + ], + [ + -0.4411730523225211, + 0.607222613015801, + 0.0 + ], + [ + 0.4411730523225211, + -0.607222613015801, + -0.46387679886902344 + ], + [ + 0.4411730523225211, + -0.607222613015801, + 0.0 + ], + [ + 0.4411730523225211, + 0.607222613015801, + -0.46387679886902344 + ], + [ + 0.4411730523225211, + 0.607222613015801, + 0.0 + ], + [ + -0.3192358196446834, + -0.23193839943451172, + 0.24387446535567534 + ], + [ + -0.3192358196446834, + 0.23193839943451172, + 0.24387446535567534 + ], + [ + -0.7138329935783748, + -0.23193839943451172, + -0.46387679886902344 + ], + [ + -0.7138329935783748, + -0.23193839943451172, + 0.0 + ], + [ + -0.7138329935783748, + 0.23193839943451172, + -0.46387679886902344 + ], + [ + -0.7138329935783748, + 0.23193839943451172, + 0.0 + ], + [ + 0.7138329935783748, + -0.23193839943451172, + -0.46387679886902344 + ], + [ + 0.7138329935783748, + -0.23193839943451172, + 0.0 + ], + [ + 0.7138329935783748, + 0.23193839943451172, + -0.46387679886902344 + ], + [ + 0.7138329935783748, + 0.23193839943451172, + 0.0 + ] + ], + "short_name": "J20" + }, + "Elongated Pentagonal Dipyramid": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + 0.0, + -0.7744386598601951 + ], + [ + 0.0, + 0.0, + 0.7744386598601951 + ], + [ + 0.6422510385476459, + 0.0, + -0.37750568872783097 + ], + [ + 0.6422510385476459, + 0.0, + 0.37750568872783097 + ], + [ + 0.19846648556618204, + -0.6108170353080686, + -0.37750568872783097 + ], + [ + 0.19846648556618204, + -0.6108170353080686, + 0.37750568872783097 + ], + [ + 0.19846648556618204, + 0.6108170353080686, + -0.37750568872783097 + ], + [ + 0.19846648556618204, + 0.6108170353080686, + 0.37750568872783097 + ], + [ + -0.519592004840005, + -0.37750568872783097, + -0.37750568872783097 + ], + [ + -0.519592004840005, + -0.37750568872783097, + 0.37750568872783097 + ], + [ + -0.519592004840005, + 0.37750568872783097, + -0.37750568872783097 + ], + [ + -0.519592004840005, + 0.37750568872783097, + 0.37750568872783097 + ] + ], + "short_name": "J16" + }, + "Elongated Pentagonal Gyrobicupola": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.70014653987575, + -0.21635717937442353 + ], + [ + 0.0, + -0.70014653987575, + 0.21635717937442353 + ], + [ + 0.0, + 0.70014653987575, + -0.21635717937442353 + ], + [ + 0.0, + 0.70014653987575, + 0.21635717937442353 + ], + [ + -0.29779011005509526, + -0.21635717937442353, + 0.4438485804293727 + ], + [ + -0.29779011005509526, + 0.21635717937442353, + 0.4438485804293727 + ], + [ + 0.29779011005509526, + -0.21635717937442353, + -0.4438485804293727 + ], + [ + 0.29779011005509526, + 0.21635717937442353, + -0.4438485804293727 + ], + [ + -0.3680888190552413, + 0.0, + -0.4438485804293727 + ], + [ + 0.3680888190552413, + 0.0, + 0.4438485804293727 + ], + [ + -0.11374570052747456, + -0.350073269937875, + -0.4438485804293727 + ], + [ + -0.11374570052747456, + 0.350073269937875, + -0.4438485804293727 + ], + [ + 0.11374570052747456, + -0.350073269937875, + 0.4438485804293727 + ], + [ + 0.11374570052747456, + 0.350073269937875, + 0.4438485804293727 + ], + [ + -0.41153581058256977, + -0.5664304493122986, + -0.21635717937442353 + ], + [ + -0.41153581058256977, + -0.5664304493122986, + 0.21635717937442353 + ], + [ + -0.41153581058256977, + 0.5664304493122986, + -0.21635717937442353 + ], + [ + -0.41153581058256977, + 0.5664304493122986, + 0.21635717937442353 + ], + [ + 0.41153581058256977, + -0.5664304493122986, + -0.21635717937442353 + ], + [ + 0.41153581058256977, + -0.5664304493122986, + 0.21635717937442353 + ], + [ + 0.41153581058256977, + 0.5664304493122986, + -0.21635717937442353 + ], + [ + 0.41153581058256977, + 0.5664304493122986, + 0.21635717937442353 + ], + [ + -0.6658789291103366, + -0.21635717937442353, + -0.21635717937442353 + ], + [ + -0.6658789291103366, + -0.21635717937442353, + 0.21635717937442353 + ], + [ + -0.6658789291103366, + 0.21635717937442353, + -0.21635717937442353 + ], + [ + -0.6658789291103366, + 0.21635717937442353, + 0.21635717937442353 + ], + [ + 0.6658789291103366, + -0.21635717937442353, + -0.21635717937442353 + ], + [ + 0.6658789291103366, + -0.21635717937442353, + 0.21635717937442353 + ], + [ + 0.6658789291103366, + 0.21635717937442353, + -0.21635717937442353 + ], + [ + 0.6658789291103366, + 0.21635717937442353, + 0.21635717937442353 + ] + ], + "short_name": "J39" + }, + "Elongated Pentagonal Gyrobirotunda": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.5816227876952831, + -0.17973132571357453 + ], + [ + 0.0, + -0.5816227876952831, + 0.17973132571357453 + ], + [ + 0.0, + 0.5816227876952831, + -0.17973132571357453 + ], + [ + 0.0, + 0.5816227876952831, + 0.17973132571357453 + ], + [ + -0.15288859750443595, + -0.47054271956121607, + -0.4855085207224465 + ], + [ + -0.15288859750443595, + 0.47054271956121607, + -0.4855085207224465 + ], + [ + 0.15288859750443595, + -0.47054271956121607, + 0.4855085207224465 + ], + [ + 0.15288859750443595, + 0.47054271956121607, + 0.4855085207224465 + ], + [ + -0.24737894725447973, + -0.17973132571357453, + -0.6744892202225341 + ], + [ + -0.24737894725447973, + 0.17973132571357453, + -0.6744892202225341 + ], + [ + 0.24737894725447973, + -0.17973132571357453, + 0.6744892202225341 + ], + [ + 0.24737894725447973, + 0.17973132571357453, + 0.6744892202225341 + ], + [ + -0.3057771950088719, + 0.0, + 0.6744892202225341 + ], + [ + 0.3057771950088719, + 0.0, + -0.6744892202225341 + ], + [ + -0.4002675447589156, + -0.29081139384764154, + 0.4855085207224465 + ], + [ + -0.4002675447589156, + 0.29081139384764154, + 0.4855085207224465 + ], + [ + 0.4002675447589156, + -0.29081139384764154, + -0.4855085207224465 + ], + [ + 0.4002675447589156, + 0.29081139384764154, + -0.4855085207224465 + ], + [ + -0.09449034975004376, + -0.29081139384764154, + 0.6744892202225341 + ], + [ + -0.09449034975004376, + 0.29081139384764154, + 0.6744892202225341 + ], + [ + 0.09449034975004376, + -0.29081139384764154, + -0.6744892202225341 + ], + [ + 0.09449034975004376, + 0.29081139384764154, + -0.6744892202225341 + ], + [ + -0.3418692970045235, + -0.47054271956121607, + -0.17973132571357453 + ], + [ + -0.3418692970045235, + -0.47054271956121607, + 0.17973132571357453 + ], + [ + -0.3418692970045235, + 0.47054271956121607, + -0.17973132571357453 + ], + [ + -0.3418692970045235, + 0.47054271956121607, + 0.17973132571357453 + ], + [ + 0.3418692970045235, + -0.47054271956121607, + -0.17973132571357453 + ], + [ + 0.3418692970045235, + -0.47054271956121607, + 0.17973132571357453 + ], + [ + 0.3418692970045235, + 0.47054271956121607, + -0.17973132571357453 + ], + [ + 0.3418692970045235, + 0.47054271956121607, + 0.17973132571357453 + ], + [ + -0.5531561422633516, + -0.17973132571357453, + -0.17973132571357453 + ], + [ + -0.5531561422633516, + -0.17973132571357453, + 0.17973132571357453 + ], + [ + -0.5531561422633516, + 0.17973132571357453, + -0.17973132571357453 + ], + [ + -0.5531561422633516, + 0.17973132571357453, + 0.17973132571357453 + ], + [ + 0.5531561422633516, + -0.17973132571357453, + -0.17973132571357453 + ], + [ + 0.5531561422633516, + -0.17973132571357453, + 0.17973132571357453 + ], + [ + 0.5531561422633516, + 0.17973132571357453, + -0.17973132571357453 + ], + [ + 0.5531561422633516, + 0.17973132571357453, + 0.17973132571357453 + ], + [ + -0.49475789450895946, + 0.0, + -0.4855085207224465 + ], + [ + 0.49475789450895946, + 0.0, + 0.4855085207224465 + ] + ], + "short_name": "J43" + }, + "Elongated Pentagonal Gyrocupolarotunda": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.6300628579662175, + -0.19470013063600994 + ], + [ + 0.0, + -0.6300628579662175, + 0.19470013063600994 + ], + [ + 0.0, + 0.6300628579662175, + -0.19470013063600994 + ], + [ + 0.0, + 0.6300628579662175, + 0.19470013063600994 + ], + [ + 0.33124364702353926, + 0.0, + -0.39941996305403016 + ], + [ + 0.1023599162090101, + -0.31503142898310876, + -0.39941996305403016 + ], + [ + 0.1023599162090101, + 0.31503142898310876, + -0.39941996305403016 + ], + [ + -0.3703416559297898, + -0.5097315596191188, + -0.19470013063600994 + ], + [ + -0.3703416559297898, + -0.5097315596191188, + 0.19470013063600994 + ], + [ + -0.3703416559297898, + 0.5097315596191188, + -0.19470013063600994 + ], + [ + -0.3703416559297898, + 0.5097315596191188, + 0.19470013063600994 + ], + [ + 0.3703416559297898, + -0.5097315596191188, + -0.19470013063600994 + ], + [ + 0.3703416559297898, + -0.5097315596191188, + 0.19470013063600994 + ], + [ + 0.3703416559297898, + 0.5097315596191188, + -0.19470013063600994 + ], + [ + 0.3703416559297898, + 0.5097315596191188, + 0.19470013063600994 + ], + [ + -0.2679817397207797, + -0.19470013063600994, + -0.39941996305403016 + ], + [ + -0.2679817397207797, + 0.19470013063600994, + -0.39941996305403016 + ], + [ + -0.599225386744319, + -0.19470013063600994, + -0.19470013063600994 + ], + [ + -0.599225386744319, + -0.19470013063600994, + 0.19470013063600994 + ], + [ + -0.599225386744319, + 0.19470013063600994, + -0.19470013063600994 + ], + [ + -0.599225386744319, + 0.19470013063600994, + 0.19470013063600994 + ], + [ + 0.599225386744319, + -0.19470013063600994, + -0.19470013063600994 + ], + [ + 0.599225386744319, + -0.19470013063600994, + 0.19470013063600994 + ], + [ + 0.599225386744319, + 0.19470013063600994, + -0.19470013063600994 + ], + [ + 0.599225386744319, + 0.19470013063600994, + 0.19470013063600994 + ], + [ + 0.5359634794415594, + 0.0, + 0.5259437776595492 + ], + [ + 0.16562182351176963, + -0.5097315596191188, + 0.5259437776595492 + ], + [ + 0.16562182351176963, + 0.5097315596191188, + 0.5259437776595492 + ], + [ + -0.43360356323254934, + -0.31503142898310876, + 0.5259437776595492 + ], + [ + -0.43360356323254934, + 0.31503142898310876, + 0.5259437776595492 + ], + [ + -0.33124364702353926, + 0.0, + 0.7306636100775695 + ], + [ + -0.1023599162090101, + -0.31503142898310876, + 0.7306636100775695 + ], + [ + -0.1023599162090101, + 0.31503142898310876, + 0.7306636100775695 + ], + [ + 0.2679817397207797, + -0.19470013063600994, + 0.7306636100775695 + ], + [ + 0.2679817397207797, + 0.19470013063600994, + 0.7306636100775695 + ] + ], + "short_name": "J41" + }, + "Elongated Pentagonal Orthobicupola": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.70014653987575, + -0.21635717937442353 + ], + [ + 0.0, + -0.70014653987575, + 0.21635717937442353 + ], + [ + 0.0, + 0.70014653987575, + -0.21635717937442353 + ], + [ + 0.0, + 0.70014653987575, + 0.21635717937442353 + ], + [ + 0.3680888190552413, + 0.0, + -0.4438485804293727 + ], + [ + 0.3680888190552413, + 0.0, + 0.4438485804293727 + ], + [ + 0.11374570052747456, + -0.350073269937875, + -0.4438485804293727 + ], + [ + 0.11374570052747456, + -0.350073269937875, + 0.4438485804293727 + ], + [ + 0.11374570052747456, + 0.350073269937875, + -0.4438485804293727 + ], + [ + 0.11374570052747456, + 0.350073269937875, + 0.4438485804293727 + ], + [ + -0.41153581058256977, + -0.5664304493122986, + -0.21635717937442353 + ], + [ + -0.41153581058256977, + -0.5664304493122986, + 0.21635717937442353 + ], + [ + -0.41153581058256977, + 0.5664304493122986, + -0.21635717937442353 + ], + [ + -0.41153581058256977, + 0.5664304493122986, + 0.21635717937442353 + ], + [ + 0.41153581058256977, + -0.5664304493122986, + -0.21635717937442353 + ], + [ + 0.41153581058256977, + -0.5664304493122986, + 0.21635717937442353 + ], + [ + 0.41153581058256977, + 0.5664304493122986, + -0.21635717937442353 + ], + [ + 0.41153581058256977, + 0.5664304493122986, + 0.21635717937442353 + ], + [ + -0.29779011005509526, + -0.21635717937442353, + -0.4438485804293727 + ], + [ + -0.29779011005509526, + -0.21635717937442353, + 0.4438485804293727 + ], + [ + -0.29779011005509526, + 0.21635717937442353, + -0.4438485804293727 + ], + [ + -0.29779011005509526, + 0.21635717937442353, + 0.4438485804293727 + ], + [ + -0.6658789291103366, + -0.21635717937442353, + -0.21635717937442353 + ], + [ + -0.6658789291103366, + -0.21635717937442353, + 0.21635717937442353 + ], + [ + -0.6658789291103366, + 0.21635717937442353, + -0.21635717937442353 + ], + [ + -0.6658789291103366, + 0.21635717937442353, + 0.21635717937442353 + ], + [ + 0.6658789291103366, + -0.21635717937442353, + -0.21635717937442353 + ], + [ + 0.6658789291103366, + -0.21635717937442353, + 0.21635717937442353 + ], + [ + 0.6658789291103366, + 0.21635717937442353, + -0.21635717937442353 + ], + [ + 0.6658789291103366, + 0.21635717937442353, + 0.21635717937442353 + ] + ], + "short_name": "J38" + }, + "Elongated Pentagonal Orthobirotunda": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.5816227876952831, + -0.17973132571357453 + ], + [ + 0.0, + -0.5816227876952831, + 0.17973132571357453 + ], + [ + 0.0, + 0.5816227876952831, + -0.17973132571357453 + ], + [ + 0.0, + 0.5816227876952831, + 0.17973132571357453 + ], + [ + -0.3418692970045235, + -0.47054271956121607, + -0.17973132571357453 + ], + [ + -0.3418692970045235, + -0.47054271956121607, + 0.17973132571357453 + ], + [ + -0.3418692970045235, + 0.47054271956121607, + -0.17973132571357453 + ], + [ + -0.3418692970045235, + 0.47054271956121607, + 0.17973132571357453 + ], + [ + 0.3418692970045235, + -0.47054271956121607, + -0.17973132571357453 + ], + [ + 0.3418692970045235, + -0.47054271956121607, + 0.17973132571357453 + ], + [ + 0.3418692970045235, + 0.47054271956121607, + -0.17973132571357453 + ], + [ + 0.3418692970045235, + 0.47054271956121607, + 0.17973132571357453 + ], + [ + -0.5531561422633516, + -0.17973132571357453, + -0.17973132571357453 + ], + [ + -0.5531561422633516, + -0.17973132571357453, + 0.17973132571357453 + ], + [ + -0.5531561422633516, + 0.17973132571357453, + -0.17973132571357453 + ], + [ + -0.5531561422633516, + 0.17973132571357453, + 0.17973132571357453 + ], + [ + 0.5531561422633516, + -0.17973132571357453, + -0.17973132571357453 + ], + [ + 0.5531561422633516, + -0.17973132571357453, + 0.17973132571357453 + ], + [ + 0.5531561422633516, + 0.17973132571357453, + -0.17973132571357453 + ], + [ + 0.5531561422633516, + 0.17973132571357453, + 0.17973132571357453 + ], + [ + 0.49475789450895946, + 0.0, + -0.4855085207224465 + ], + [ + 0.49475789450895946, + 0.0, + 0.4855085207224465 + ], + [ + 0.15288859750443595, + -0.47054271956121607, + -0.4855085207224465 + ], + [ + 0.15288859750443595, + -0.47054271956121607, + 0.4855085207224465 + ], + [ + 0.15288859750443595, + 0.47054271956121607, + -0.4855085207224465 + ], + [ + 0.15288859750443595, + 0.47054271956121607, + 0.4855085207224465 + ], + [ + -0.4002675447589156, + -0.29081139384764154, + -0.4855085207224465 + ], + [ + -0.4002675447589156, + -0.29081139384764154, + 0.4855085207224465 + ], + [ + -0.4002675447589156, + 0.29081139384764154, + -0.4855085207224465 + ], + [ + -0.4002675447589156, + 0.29081139384764154, + 0.4855085207224465 + ], + [ + -0.3057771950088719, + 0.0, + -0.6744892202225341 + ], + [ + -0.3057771950088719, + 0.0, + 0.6744892202225341 + ], + [ + -0.09449034975004376, + -0.29081139384764154, + -0.6744892202225341 + ], + [ + -0.09449034975004376, + -0.29081139384764154, + 0.6744892202225341 + ], + [ + -0.09449034975004376, + 0.29081139384764154, + -0.6744892202225341 + ], + [ + -0.09449034975004376, + 0.29081139384764154, + 0.6744892202225341 + ], + [ + 0.24737894725447973, + -0.17973132571357453, + -0.6744892202225341 + ], + [ + 0.24737894725447973, + -0.17973132571357453, + 0.6744892202225341 + ], + [ + 0.24737894725447973, + 0.17973132571357453, + -0.6744892202225341 + ], + [ + 0.24737894725447973, + 0.17973132571357453, + 0.6744892202225341 + ] + ], + "short_name": "J42" + }, + "Elongated Pentagonal Orthocupolarotunda": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.6300628579662176, + -0.19470013063600997 + ], + [ + 0.0, + -0.6300628579662176, + 0.19470013063600997 + ], + [ + 0.0, + 0.6300628579662176, + -0.19470013063600997 + ], + [ + 0.0, + 0.6300628579662176, + 0.19470013063600997 + ], + [ + 0.16562182351176963, + -0.5097315596191188, + 0.5259437776595494 + ], + [ + 0.16562182351176963, + 0.5097315596191188, + 0.5259437776595494 + ], + [ + 0.26798173972077977, + -0.19470013063600997, + -0.3994199630540302 + ], + [ + 0.26798173972077977, + -0.19470013063600997, + 0.7306636100775696 + ], + [ + 0.26798173972077977, + 0.19470013063600997, + -0.3994199630540302 + ], + [ + 0.26798173972077977, + 0.19470013063600997, + 0.7306636100775696 + ], + [ + -0.33124364702353926, + 0.0, + -0.3994199630540302 + ], + [ + -0.33124364702353926, + 0.0, + 0.7306636100775696 + ], + [ + -0.4336035632325494, + -0.3150314289831088, + 0.5259437776595494 + ], + [ + -0.4336035632325494, + 0.3150314289831088, + 0.5259437776595494 + ], + [ + -0.10235991620901011, + -0.3150314289831088, + -0.3994199630540302 + ], + [ + -0.10235991620901011, + -0.3150314289831088, + 0.7306636100775696 + ], + [ + -0.10235991620901011, + 0.3150314289831088, + -0.3994199630540302 + ], + [ + -0.10235991620901011, + 0.3150314289831088, + 0.7306636100775696 + ], + [ + -0.37034165592978985, + -0.5097315596191188, + -0.19470013063600997 + ], + [ + -0.37034165592978985, + -0.5097315596191188, + 0.19470013063600997 + ], + [ + -0.37034165592978985, + 0.5097315596191188, + -0.19470013063600997 + ], + [ + -0.37034165592978985, + 0.5097315596191188, + 0.19470013063600997 + ], + [ + 0.37034165592978985, + -0.5097315596191188, + -0.19470013063600997 + ], + [ + 0.37034165592978985, + -0.5097315596191188, + 0.19470013063600997 + ], + [ + 0.37034165592978985, + 0.5097315596191188, + -0.19470013063600997 + ], + [ + 0.37034165592978985, + 0.5097315596191188, + 0.19470013063600997 + ], + [ + -0.5992253867443191, + -0.19470013063600997, + -0.19470013063600997 + ], + [ + -0.5992253867443191, + -0.19470013063600997, + 0.19470013063600997 + ], + [ + -0.5992253867443191, + 0.19470013063600997, + -0.19470013063600997 + ], + [ + -0.5992253867443191, + 0.19470013063600997, + 0.19470013063600997 + ], + [ + 0.5992253867443191, + -0.19470013063600997, + -0.19470013063600997 + ], + [ + 0.5992253867443191, + -0.19470013063600997, + 0.19470013063600997 + ], + [ + 0.5992253867443191, + 0.19470013063600997, + -0.19470013063600997 + ], + [ + 0.5992253867443191, + 0.19470013063600997, + 0.19470013063600997 + ], + [ + 0.5359634794415595, + 0.0, + 0.5259437776595494 + ] + ], + "short_name": "J40" + }, + "Elongated Pentagonal Pyramid": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + 0.0, + 1.2065695672061325 + ], + [ + 0.6727065926127129, + 0.0, + 0.0 + ], + [ + 0.6727065926127129, + 0.0, + 0.7908140285153469 + ], + [ + 0.20787776934539276, + -0.6397819884590299, + 0.0 + ], + [ + 0.20787776934539276, + -0.6397819884590299, + 0.7908140285153469 + ], + [ + 0.20787776934539276, + 0.6397819884590299, + 0.0 + ], + [ + 0.20787776934539276, + 0.6397819884590299, + 0.7908140285153469 + ], + [ + -0.5442310656517493, + -0.39540701425767344, + 0.0 + ], + [ + -0.5442310656517493, + -0.39540701425767344, + 0.7908140285153469 + ], + [ + -0.5442310656517493, + 0.39540701425767344, + 0.0 + ], + [ + -0.5442310656517493, + 0.39540701425767344, + 0.7908140285153469 + ] + ], + "short_name": "J9" + }, + "Elongated Pentagonal Rotunda": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.6618374911263416, + -0.409038064545036 + ], + [ + 0.0, + -0.6618374911263416, + 0.0 + ], + [ + 0.0, + 0.6618374911263416, + -0.409038064545036 + ], + [ + 0.0, + 0.6618374911263416, + 0.0 + ], + [ + -0.3890183166983141, + -0.5354377778356888, + -0.409038064545036 + ], + [ + -0.3890183166983141, + -0.5354377778356888, + 0.0 + ], + [ + -0.3890183166983141, + 0.5354377778356888, + -0.409038064545036 + ], + [ + -0.3890183166983141, + 0.5354377778356888, + 0.0 + ], + [ + 0.3890183166983141, + -0.5354377778356888, + -0.409038064545036 + ], + [ + 0.3890183166983141, + -0.5354377778356888, + 0.0 + ], + [ + 0.3890183166983141, + 0.5354377778356888, + -0.409038064545036 + ], + [ + 0.3890183166983141, + 0.5354377778356888, + 0.0 + ], + [ + -0.629444858664143, + -0.204519032272518, + -0.409038064545036 + ], + [ + -0.629444858664143, + -0.204519032272518, + 0.0 + ], + [ + -0.629444858664143, + 0.204519032272518, + -0.409038064545036 + ], + [ + -0.629444858664143, + 0.204519032272518, + 0.0 + ], + [ + 0.629444858664143, + -0.204519032272518, + -0.409038064545036 + ], + [ + 0.629444858664143, + -0.204519032272518, + 0.0 + ], + [ + 0.629444858664143, + 0.204519032272518, + -0.409038064545036 + ], + [ + 0.629444858664143, + 0.204519032272518, + 0.0 + ], + [ + 0.5629925968243085, + 0.0, + 0.3479485602519887 + ], + [ + 0.17397428012599436, + -0.5354377778356888, + 0.3479485602519887 + ], + [ + 0.17397428012599436, + 0.5354377778356888, + 0.3479485602519887 + ], + [ + -0.4554705785381486, + -0.3309187455631708, + 0.3479485602519887 + ], + [ + -0.4554705785381486, + 0.3309187455631708, + 0.3479485602519887 + ], + [ + -0.3479485602519887, + 0.0, + 0.5629925968243085 + ], + [ + -0.10752201828615986, + -0.3309187455631708, + 0.5629925968243085 + ], + [ + -0.10752201828615986, + 0.3309187455631708, + 0.5629925968243085 + ], + [ + 0.28149629841215423, + -0.204519032272518, + 0.5629925968243085 + ], + [ + 0.28149629841215423, + 0.204519032272518, + 0.5629925968243085 + ] + ], + "short_name": "J21" + }, + "Elongated Square Cupola": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.37376246190547224, + 0.37376246190547224 + ], + [ + 0.0, + 0.37376246190547224, + 0.37376246190547224 + ], + [ + -0.37376246190547224, + 0.0, + 0.37376246190547224 + ], + [ + 0.37376246190547224, + 0.0, + 0.37376246190547224 + ], + [ + 0.2642899713663381, + 0.6380524332718103, + -0.5285799427326762 + ], + [ + 0.2642899713663381, + 0.6380524332718103, + 0.0 + ], + [ + -0.2642899713663381, + 0.6380524332718103, + -0.5285799427326762 + ], + [ + -0.2642899713663381, + 0.6380524332718103, + 0.0 + ], + [ + -0.6380524332718103, + 0.2642899713663381, + -0.5285799427326762 + ], + [ + -0.6380524332718103, + 0.2642899713663381, + 0.0 + ], + [ + -0.6380524332718103, + -0.2642899713663381, + -0.5285799427326762 + ], + [ + -0.6380524332718103, + -0.2642899713663381, + 0.0 + ], + [ + -0.2642899713663381, + -0.6380524332718103, + -0.5285799427326762 + ], + [ + -0.2642899713663381, + -0.6380524332718103, + 0.0 + ], + [ + 0.2642899713663381, + -0.6380524332718103, + -0.5285799427326762 + ], + [ + 0.2642899713663381, + -0.6380524332718103, + 0.0 + ], + [ + 0.6380524332718103, + -0.2642899713663381, + -0.5285799427326762 + ], + [ + 0.6380524332718103, + -0.2642899713663381, + 0.0 + ], + [ + 0.6380524332718103, + 0.2642899713663381, + -0.5285799427326762 + ], + [ + 0.6380524332718103, + 0.2642899713663381, + 0.0 + ] + ], + "short_name": "J19" + }, + "Elongated Square Dipyramid": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + 0.0, + -1.0612922536238576 + ], + [ + 0.0, + 0.0, + 1.0612922536238576 + ], + [ + 0.0, + -0.6216906085313493, + -0.4396016450925084 + ], + [ + 0.0, + -0.6216906085313493, + 0.4396016450925084 + ], + [ + 0.0, + 0.6216906085313493, + -0.4396016450925084 + ], + [ + 0.0, + 0.6216906085313493, + 0.4396016450925084 + ], + [ + -0.6216906085313493, + 0.0, + -0.4396016450925084 + ], + [ + -0.6216906085313493, + 0.0, + 0.4396016450925084 + ], + [ + 0.6216906085313493, + 0.0, + -0.4396016450925084 + ], + [ + 0.6216906085313493, + 0.0, + 0.4396016450925084 + ] + ], + "short_name": "J15" + }, + "Elongated Square Gyrobicupola": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.2429760130015836, + -0.2429760130015836, + -0.5865959859197646 + ], + [ + -0.2429760130015836, + 0.2429760130015836, + -0.5865959859197646 + ], + [ + 0.0, + -0.34361997291818097, + 0.5865959859197646 + ], + [ + 0.0, + 0.34361997291818097, + 0.5865959859197646 + ], + [ + 0.2429760130015836, + -0.2429760130015836, + -0.5865959859197646 + ], + [ + 0.2429760130015836, + 0.2429760130015836, + -0.5865959859197646 + ], + [ + -0.34361997291818097, + 0.0, + 0.5865959859197646 + ], + [ + 0.34361997291818097, + 0.0, + 0.5865959859197646 + ], + [ + 0.2429760130015836, + 0.5865959859197646, + -0.2429760130015836 + ], + [ + 0.2429760130015836, + 0.5865959859197646, + 0.2429760130015836 + ], + [ + -0.2429760130015836, + 0.5865959859197646, + -0.2429760130015836 + ], + [ + -0.2429760130015836, + 0.5865959859197646, + 0.2429760130015836 + ], + [ + -0.5865959859197646, + 0.2429760130015836, + -0.2429760130015836 + ], + [ + -0.5865959859197646, + 0.2429760130015836, + 0.2429760130015836 + ], + [ + -0.5865959859197646, + -0.2429760130015836, + -0.2429760130015836 + ], + [ + -0.5865959859197646, + -0.2429760130015836, + 0.2429760130015836 + ], + [ + -0.2429760130015836, + -0.5865959859197646, + -0.2429760130015836 + ], + [ + -0.2429760130015836, + -0.5865959859197646, + 0.2429760130015836 + ], + [ + 0.2429760130015836, + -0.5865959859197646, + -0.2429760130015836 + ], + [ + 0.2429760130015836, + -0.5865959859197646, + 0.2429760130015836 + ], + [ + 0.5865959859197646, + -0.2429760130015836, + -0.2429760130015836 + ], + [ + 0.5865959859197646, + -0.2429760130015836, + 0.2429760130015836 + ], + [ + 0.5865959859197646, + 0.2429760130015836, + -0.2429760130015836 + ], + [ + 0.5865959859197646, + 0.2429760130015836, + 0.2429760130015836 + ] + ], + "short_name": "J37" + }, + "Elongated Square Pyramid": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + 0.0, + 1.590826220203367 + ], + [ + 0.0, + -0.6589417957869623, + 0.0 + ], + [ + 0.0, + -0.6589417957869623, + 0.9318844244164046 + ], + [ + 0.0, + 0.6589417957869623, + 0.0 + ], + [ + 0.0, + 0.6589417957869623, + 0.9318844244164046 + ], + [ + -0.6589417957869623, + 0.0, + 0.0 + ], + [ + -0.6589417957869623, + 0.0, + 0.9318844244164046 + ], + [ + 0.6589417957869623, + 0.0, + 0.0 + ], + [ + 0.6589417957869623, + 0.0, + 0.9318844244164046 + ] + ], + "short_name": "J8" + }, + "Elongated Triangular Cupola": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.6421455575221124, + -0.6421455575221124 + ], + [ + 0.0, + -0.6421455575221124, + 0.0 + ], + [ + 0.0, + 0.6421455575221124, + -0.6421455575221124 + ], + [ + 0.0, + 0.6421455575221124, + 0.0 + ], + [ + -0.18537145524715698, + -0.3210727787610562, + 0.5243096521747332 + ], + [ + -0.18537145524715698, + 0.3210727787610562, + 0.5243096521747332 + ], + [ + 0.37074291049431396, + 0.0, + 0.5243096521747332 + ], + [ + -0.5561143657414709, + -0.3210727787610562, + -0.6421455575221124 + ], + [ + -0.5561143657414709, + -0.3210727787610562, + 0.0 + ], + [ + -0.5561143657414709, + 0.3210727787610562, + -0.6421455575221124 + ], + [ + -0.5561143657414709, + 0.3210727787610562, + 0.0 + ], + [ + 0.5561143657414709, + -0.3210727787610562, + -0.6421455575221124 + ], + [ + 0.5561143657414709, + -0.3210727787610562, + 0.0 + ], + [ + 0.5561143657414709, + 0.3210727787610562, + -0.6421455575221124 + ], + [ + 0.5561143657414709, + 0.3210727787610562, + 0.0 + ] + ], + "short_name": "J18" + }, + "Elongated Triangular Dipyramid": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + 0.0, + -1.505472136835881 + ], + [ + 0.0, + 0.0, + 1.505472136835881 + ], + [ + -0.3301127993994366, + -0.5717721407886169, + -0.5717721407886169 + ], + [ + -0.3301127993994366, + -0.5717721407886169, + 0.5717721407886169 + ], + [ + -0.3301127993994366, + 0.5717721407886169, + -0.5717721407886169 + ], + [ + -0.3301127993994366, + 0.5717721407886169, + 0.5717721407886169 + ], + [ + 0.6602255987988732, + 0.0, + -0.5717721407886169 + ], + [ + 0.6602255987988732, + 0.0, + 0.5717721407886169 + ] + ], + "short_name": "J14" + }, + "Elongated Triangular Gyrobicupola": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.5865646598202142, + -0.2932823299101071 + ], + [ + 0.0, + -0.5865646598202142, + 0.2932823299101071 + ], + [ + 0.0, + 0.5865646598202142, + -0.2932823299101071 + ], + [ + 0.0, + 0.5865646598202142, + 0.2932823299101071 + ], + [ + -0.16932663212216098, + -0.2932823299101071, + 0.7722103691463466 + ], + [ + -0.16932663212216098, + 0.2932823299101071, + 0.7722103691463466 + ], + [ + 0.16932663212216098, + -0.2932823299101071, + -0.7722103691463466 + ], + [ + 0.33865326424432196, + 0.0, + 0.7722103691463466 + ], + [ + -0.5079798963664829, + -0.2932823299101071, + -0.2932823299101071 + ], + [ + -0.5079798963664829, + -0.2932823299101071, + 0.2932823299101071 + ], + [ + -0.5079798963664829, + 0.2932823299101071, + -0.2932823299101071 + ], + [ + -0.5079798963664829, + 0.2932823299101071, + 0.2932823299101071 + ], + [ + 0.5079798963664829, + -0.2932823299101071, + -0.2932823299101071 + ], + [ + 0.5079798963664829, + -0.2932823299101071, + 0.2932823299101071 + ], + [ + 0.5079798963664829, + 0.2932823299101071, + -0.2932823299101071 + ], + [ + 0.5079798963664829, + 0.2932823299101071, + 0.2932823299101071 + ], + [ + -0.33865326424432196, + 0.0, + -0.7722103691463466 + ], + [ + 0.16932663212216098, + 0.2932823299101071, + -0.7722103691463466 + ] + ], + "short_name": "J36" + }, + "Elongated Triangular Orthobicupola": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.5865646598202142, + -0.2932823299101071 + ], + [ + 0.0, + -0.5865646598202142, + 0.2932823299101071 + ], + [ + 0.0, + 0.5865646598202142, + -0.2932823299101071 + ], + [ + 0.0, + 0.5865646598202142, + 0.2932823299101071 + ], + [ + -0.16932663212216098, + -0.2932823299101071, + -0.7722103691463466 + ], + [ + -0.16932663212216098, + -0.2932823299101071, + 0.7722103691463466 + ], + [ + -0.16932663212216098, + 0.2932823299101071, + -0.7722103691463466 + ], + [ + -0.16932663212216098, + 0.2932823299101071, + 0.7722103691463466 + ], + [ + 0.33865326424432196, + 0.0, + -0.7722103691463466 + ], + [ + 0.33865326424432196, + 0.0, + 0.7722103691463466 + ], + [ + -0.5079798963664829, + -0.2932823299101071, + -0.2932823299101071 + ], + [ + -0.5079798963664829, + -0.2932823299101071, + 0.2932823299101071 + ], + [ + -0.5079798963664829, + 0.2932823299101071, + -0.2932823299101071 + ], + [ + -0.5079798963664829, + 0.2932823299101071, + 0.2932823299101071 + ], + [ + 0.5079798963664829, + -0.2932823299101071, + -0.2932823299101071 + ], + [ + 0.5079798963664829, + -0.2932823299101071, + 0.2932823299101071 + ], + [ + 0.5079798963664829, + 0.2932823299101071, + -0.2932823299101071 + ], + [ + 0.5079798963664829, + 0.2932823299101071, + 0.2932823299101071 + ] + ], + "short_name": "J35" + }, + "Elongated Triangular Pyramid": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + 0.0, + 2.21591534579912 + ], + [ + -0.35215021454792583, + -0.6099420634932883, + 0.0 + ], + [ + -0.35215021454792583, + -0.6099420634932883, + 1.2198841269865766 + ], + [ + -0.35215021454792583, + 0.6099420634932883, + 0.0 + ], + [ + -0.35215021454792583, + 0.6099420634932883, + 1.2198841269865766 + ], + [ + 0.7043004290958517, + 0.0, + 0.0 + ], + [ + 0.7043004290958517, + 0.0, + 1.2198841269865766 + ] + ], + "short_name": "J7" + }, + "Gyrate Bidiminished Rhombicosidodecahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.15009435383073874, + -0.15009435383073874, + -0.6358098858659152 + ], + [ + -0.15009435383073874, + -0.15009435383073874, + 0.6358098858659152 + ], + [ + -0.15009435383073874, + 0.15009435383073874, + -0.6358098858659152 + ], + [ + -0.15009435383073874, + 0.15009435383073874, + 0.6358098858659152 + ], + [ + -0.15009435383073874, + -0.6358098858659152, + -0.15009435383073874 + ], + [ + -0.15009435383073874, + 0.6358098858659152, + -0.15009435383073874 + ], + [ + 0.0, + -0.39295211984832706, + -0.5430464736790658 + ], + [ + 0.0, + 0.392952119848327, + -0.5430464736790658 + ], + [ + 0.10860929473581316, + 0.0, + -0.6614490624118772 + ], + [ + 0.15009435383073874, + -0.15009435383073874, + 0.6358098858659152 + ], + [ + 0.2587036485665519, + 0.24285776601758827, + -0.5686856502250277 + ], + [ + 0.15009435383073874, + 0.15009435383073874, + 0.6358098858659152 + ], + [ + 0.15009435383073874, + -0.6358098858659152, + -0.15009435383073874 + ], + [ + 0.15009435383073874, + 0.6358098858659152, + -0.15009435383073874 + ], + [ + -0.5430464736790658, + 0.0, + -0.39295211984832706 + ], + [ + -0.5430464736790658, + 0.0, + 0.392952119848327 + ], + [ + -0.24285776601758827, + -0.48571553203517653, + -0.39295211984832706 + ], + [ + -0.24285776601758827, + 0.48571553203517653, + -0.39295211984832706 + ], + [ + -0.48571553203517653, + -0.39295211984832706, + -0.24285776601758827 + ], + [ + -0.48571553203517653, + -0.39295211984832706, + 0.24285776601758827 + ], + [ + -0.48571553203517653, + 0.392952119848327, + -0.24285776601758827 + ], + [ + -0.48571553203517653, + 0.392952119848327, + 0.24285776601758827 + ], + [ + -0.6358098858659152, + -0.15009435383073874, + -0.15009435383073874 + ], + [ + -0.6358098858659152, + -0.15009435383073874, + 0.15009435383073874 + ], + [ + -0.6358098858659152, + 0.15009435383073874, + -0.15009435383073874 + ], + [ + -0.6358098858659152, + 0.15009435383073874, + 0.15009435383073874 + ], + [ + -0.39295211984832706, + -0.5430464736790658, + 0.0 + ], + [ + -0.39295211984832706, + -0.24285776601758827, + -0.48571553203517653 + ], + [ + -0.39295211984832706, + -0.24285776601758827, + 0.48571553203517653 + ], + [ + -0.39295211984832706, + 0.24285776601758827, + -0.48571553203517653 + ], + [ + -0.39295211984832706, + 0.24285776601758827, + 0.48571553203517653 + ], + [ + -0.39295211984832706, + 0.5430464736790658, + 0.0 + ], + [ + 0.24285776601758827, + -0.48571553203517653, + -0.39295211984832706 + ], + [ + 0.24285776601758827, + 0.48571553203517653, + -0.39295211984832706 + ], + [ + 0.48571553203517653, + -0.39295211984832706, + -0.24285776601758827 + ], + [ + 0.48571553203517653, + -0.39295211984832706, + 0.24285776601758827 + ], + [ + 0.48571553203517653, + 0.392952119848327, + -0.24285776601758827 + ], + [ + 0.48571553203517653, + 0.392952119848327, + 0.24285776601758827 + ], + [ + 0.6358098858659152, + -0.15009435383073874, + -0.15009435383073874 + ], + [ + 0.6358098858659152, + -0.15009435383073874, + 0.15009435383073874 + ], + [ + 0.6358098858659152, + 0.15009435383073874, + -0.15009435383073874 + ], + [ + 0.6358098858659152, + 0.15009435383073874, + 0.15009435383073874 + ], + [ + 0.392952119848327, + -0.5430464736790658, + 0.0 + ], + [ + 0.2587036485665519, + -0.24285776601758827, + -0.5686856502250277 + ], + [ + 0.392952119848327, + -0.24285776601758827, + 0.48571553203517653 + ], + [ + 0.5015614145841402, + 0.15009435383073874, + -0.41859129639428894 + ], + [ + 0.392952119848327, + 0.24285776601758827, + 0.48571553203517653 + ], + [ + 0.392952119848327, + 0.5430464736790658, + 0.0 + ], + [ + 0.5015614145841402, + -0.15009435383073874, + -0.41859129639428894 + ], + [ + 0.5430464736790658, + 0.0, + 0.392952119848327 + ] + ], + "short_name": "J82" + }, + "Gyrate Rhombicosidodecahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.24547101952821324, + 0.5957706792746074 + ], + [ + 0.4669136253678442, + 0.0, + -0.44406124595308233 + ], + [ + -0.2334568126839221, + -0.07585471666076248, + 0.5957706792746074 + ], + [ + 0.3777410578278035, + 0.27444494308563155, + -0.44406124595308233 + ], + [ + 0.2334568126839221, + -0.5667967557171889, + 0.1985902264248691 + ], + [ + 0.3777410578278035, + -0.5199159626138448, + -0.04688079310334414 + ], + [ + -0.1442842451438814, + 0.5957706792746074, + 0.1985902264248691 + ], + [ + 0.0, + 0.6426514723779514, + -0.04688079310334414 + ], + [ + -0.1442842451438814, + -0.44406124595308233, + 0.44406124595308233 + ], + [ + 0.3777410578278035, + -0.27444494308563155, + -0.44406124595308233 + ], + [ + -0.3777410578278035, + 0.27444494308563155, + 0.44406124595308233 + ], + [ + 0.1442842451438814, + 0.44406124595308233, + -0.44406124595308233 + ], + [ + -0.3777410578278035, + -0.27444494308563155, + 0.44406124595308233 + ], + [ + 0.2334568126839221, + -0.07585471666076248, + -0.5957706792746074 + ], + [ + -0.4669136253678442, + 0.0, + 0.44406124595308233 + ], + [ + 0.1442842451438814, + 0.1985902264248691, + -0.5957706792746074 + ], + [ + 0.0, + -0.6426514723779514, + 0.04688079310334414 + ], + [ + 0.1442842451438814, + -0.5957706792746074, + -0.1985902264248691 + ], + [ + -0.3777410578278035, + 0.5199159626138448, + 0.04688079310334414 + ], + [ + -0.2334568126839221, + 0.5667967557171889, + -0.1985902264248691 + ], + [ + 0.1442842451438814, + 0.1985902264248691, + 0.5957706792746074 + ], + [ + 0.6111978705117256, + 0.1985902264248691, + -0.04688079310334414 + ], + [ + 0.1442842451438814, + -0.44406124595308233, + 0.44406124595308233 + ], + [ + 0.5220253029716849, + -0.3213257361889757, + -0.1985902264248691 + ], + [ + -0.1442842451438814, + 0.44406124595308233, + 0.44406124595308233 + ], + [ + 0.2334568126839221, + 0.5667967557171889, + -0.1985902264248691 + ], + [ + 0.3777410578278035, + -0.27444494308563155, + 0.44406124595308233 + ], + [ + 0.6111978705117256, + -0.1985902264248691, + 0.04688079310334414 + ], + [ + 0.1442842451438814, + 0.44406124595308233, + 0.44406124595308233 + ], + [ + 0.3777410578278035, + 0.5199159626138448, + 0.04688079310334414 + ], + [ + 0.4669136253678442, + 0.0, + 0.44406124595308233 + ], + [ + 0.6111978705117256, + 0.04688079310334414, + 0.1985902264248691 + ], + [ + 0.3777410578278035, + 0.27444494308563155, + 0.44406124595308233 + ], + [ + 0.5220253029716849, + 0.3213257361889757, + 0.1985902264248691 + ], + [ + 0.4669136253678442, + -0.3971804528497382, + 0.1985902264248691 + ], + [ + 0.2334568126839221, + -0.07585471666076248, + 0.5957706792746074 + ], + [ + 0.6111978705117256, + -0.04688079310334414, + -0.1985902264248691 + ], + [ + -0.1442842451438814, + 0.1985902264248691, + 0.5957706792746074 + ], + [ + 0.4669136253678442, + 0.3971804528497382, + -0.1985902264248691 + ], + [ + 0.1442842451438814, + 0.5957706792746074, + 0.1985902264248691 + ], + [ + -0.2334568126839221, + -0.5667967557171889, + 0.1985902264248691 + ], + [ + 0.1442842451438814, + -0.44406124595308233, + -0.44406124595308233 + ], + [ + -0.5220253029716849, + 0.3213257361889757, + 0.1985902264248691 + ], + [ + -0.1442842451438814, + 0.44406124595308233, + -0.44406124595308233 + ], + [ + -0.3777410578278036, + -0.5199159626138448, + -0.04688079310334414 + ], + [ + -0.1442842451438814, + -0.44406124595308233, + -0.44406124595308233 + ], + [ + -0.6111978705117256, + 0.1985902264248691, + -0.04688079310334414 + ], + [ + -0.3777410578278035, + 0.27444494308563155, + -0.44406124595308233 + ], + [ + -0.5220253029716849, + -0.3213257361889757, + -0.1985902264248691 + ], + [ + -0.3777410578278035, + -0.27444494308563155, + -0.44406124595308233 + ], + [ + -0.6111978705117256, + -0.04688079310334414, + -0.1985902264248691 + ], + [ + -0.4669136253678442, + 0.0, + -0.44406124595308233 + ], + [ + -0.1442842451438814, + -0.5957706792746074, + -0.1985902264248691 + ], + [ + -0.4669136253678442, + -0.3971804528497382, + 0.1985902264248691 + ], + [ + 0.0, + -0.24547101952821324, + -0.5957706792746074 + ], + [ + -0.6111978705117256, + 0.04688079310334414, + 0.1985902264248691 + ], + [ + -0.1442842451438814, + 0.1985902264248691, + -0.5957706792746074 + ], + [ + -0.4669136253678442, + 0.3971804528497382, + -0.1985902264248691 + ], + [ + -0.6111978705117256, + -0.1985902264248691, + 0.04688079310334414 + ], + [ + -0.2334568126839221, + -0.07585471666076248, + -0.5957706792746074 + ] + ], + "short_name": "J72" + }, + "Gyrobifastigium": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.5245575317108241, + -0.5245575317108241, + 0.0 + ], + [ + -0.5245575317108241, + 0.0, + 0.9085602964160697 + ], + [ + -0.5245575317108241, + 0.5245575317108241, + 0.0 + ], + [ + 0.0, + -0.5245575317108241, + -0.9085602964160697 + ], + [ + 0.0, + 0.5245575317108241, + -0.9085602964160697 + ], + [ + 0.5245575317108241, + -0.5245575317108241, + 0.0 + ], + [ + 0.5245575317108241, + 0.0, + 0.9085602964160697 + ], + [ + 0.5245575317108241, + 0.5245575317108241, + 0.0 + ] + ], + "short_name": "J26" + }, + "Gyroelongated Pentagonal Bicupola": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.7189841498375291, + 0.0, + 0.1916059183408687 + ], + [ + -0.6837945608159132, + -0.22217832098602008, + -0.19160591834086887 + ], + [ + -0.6837945608159132, + 0.22217832098602008, + -0.19160591834086887 + ], + [ + -0.5816703959047846, + -0.4226082799065413, + 0.1916059183408687 + ], + [ + -0.5816703959047846, + 0.4226082799065413, + 0.1916059183408687 + ], + [ + -0.4226082799065413, + -0.5816703959047846, + -0.19160591834086887 + ], + [ + -0.4226082799065413, + 0.5816703959047846, + -0.19160591834086887 + ], + [ + -0.35949207491876456, + 0.11680605578074217, + 0.425218029902353 + ], + [ + -0.30580222412579916, + -0.22217832098602008, + -0.4252180299023532 + ], + [ + -0.30580222412579916, + 0.22217832098602008, + -0.4252180299023532 + ], + [ + -0.22217832098602008, + -0.6837945608159132, + 0.1916059183408687 + ], + [ + -0.22217832098602008, + -0.30580222412579916, + 0.425218029902353 + ], + [ + -0.22217832098602008, + 0.6837945608159132, + 0.1916059183408687 + ], + [ + 0.0, + -0.7189841498375291, + -0.19160591834086887 + ], + [ + 0.0, + 0.377992336690114, + 0.425218029902353 + ], + [ + 0.0, + 0.7189841498375291, + -0.19160591834086887 + ], + [ + 0.11680605578074217, + -0.35949207491876456, + -0.4252180299023532 + ], + [ + 0.11680605578074217, + 0.35949207491876456, + -0.4252180299023532 + ], + [ + 0.22217832098602008, + -0.6837945608159132, + 0.1916059183408687 + ], + [ + 0.22217832098602008, + -0.30580222412579916, + 0.425218029902353 + ], + [ + 0.22217832098602008, + 0.6837945608159132, + 0.1916059183408687 + ], + [ + 0.35949207491876456, + 0.11680605578074217, + 0.425218029902353 + ], + [ + 0.377992336690114, + 0.0, + -0.4252180299023532 + ], + [ + 0.4226082799065413, + -0.5816703959047846, + -0.19160591834086887 + ], + [ + 0.4226082799065413, + 0.5816703959047846, + -0.19160591834086887 + ], + [ + 0.5816703959047846, + -0.4226082799065413, + 0.1916059183408687 + ], + [ + 0.5816703959047846, + 0.4226082799065413, + 0.1916059183408687 + ], + [ + 0.6837945608159132, + -0.22217832098602008, + -0.19160591834086887 + ], + [ + 0.6837945608159132, + 0.22217832098602008, + -0.19160591834086887 + ], + [ + 0.7189841498375291, + 0.0, + 0.1916059183408687 + ] + ], + "short_name": "J46" + }, + "Gyroelongated Pentagonal Birotunda": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.5903895464571245, + 0.0, + -0.1573360570651369 + ], + [ + -0.5614938253105886, + -0.182440403156569, + 0.15733605706513676 + ], + [ + -0.5614938253105886, + 0.182440403156569, + 0.15733605706513676 + ], + [ + -0.47763517638513125, + -0.34702226851513973, + -0.1573360570651369 + ], + [ + -0.47763517638513125, + 0.1551930764212075, + -0.46772220990755176 + ], + [ + -0.47763517638513125, + 0.34702226851513973, + -0.1573360570651369 + ], + [ + -0.40630074888938106, + -0.29519477322856225, + 0.46772220990755176 + ], + [ + -0.40630074888938106, + 0.29519477322856225, + 0.46772220990755176 + ], + [ + -0.34702226851513973, + -0.47763517638513125, + 0.15733605706513676 + ], + [ + -0.34702226851513973, + 0.47763517638513125, + 0.15733605706513676 + ], + [ + -0.310386152842415, + 0.0, + 0.659551402001484 + ], + [ + -0.29519477322856225, + -0.40630074888938106, + -0.46772220990755176 + ], + [ + -0.29519477322856225, + -0.09591459604696612, + -0.659551402001484 + ], + [ + -0.182440403156569, + -0.5614938253105886, + -0.1573360570651369 + ], + [ + -0.182440403156569, + 0.2511076724681736, + -0.659551402001484 + ], + [ + -0.182440403156569, + 0.5614938253105886, + -0.1573360570651369 + ], + [ + -0.09591459604696612, + -0.29519477322856225, + 0.659551402001484 + ], + [ + -0.09591459604696612, + 0.29519477322856225, + 0.659551402001484 + ], + [ + 0.0, + -0.5903895464571245, + 0.15733605706513676 + ], + [ + 0.0, + -0.310386152842415, + -0.659551402001484 + ], + [ + 0.0, + 0.5022153449363472, + -0.46772220990755176 + ], + [ + 0.0, + 0.5903895464571245, + 0.15733605706513676 + ], + [ + 0.1551930764212075, + -0.47763517638513125, + 0.46772220990755176 + ], + [ + 0.1551930764212075, + 0.47763517638513125, + 0.46772220990755176 + ], + [ + 0.182440403156569, + -0.5614938253105886, + -0.1573360570651369 + ], + [ + 0.182440403156569, + 0.2511076724681736, + -0.659551402001484 + ], + [ + 0.182440403156569, + 0.5614938253105886, + -0.1573360570651369 + ], + [ + 0.2511076724681736, + -0.182440403156569, + 0.659551402001484 + ], + [ + 0.2511076724681736, + 0.182440403156569, + 0.659551402001484 + ], + [ + 0.29519477322856225, + -0.40630074888938106, + -0.46772220990755176 + ], + [ + 0.29519477322856225, + -0.09591459604696612, + -0.659551402001484 + ], + [ + 0.34702226851513973, + -0.47763517638513125, + 0.15733605706513676 + ], + [ + 0.34702226851513973, + 0.47763517638513125, + 0.15733605706513676 + ], + [ + 0.47763517638513125, + -0.34702226851513973, + -0.1573360570651369 + ], + [ + 0.47763517638513125, + 0.1551930764212075, + -0.46772220990755176 + ], + [ + 0.47763517638513125, + 0.34702226851513973, + -0.1573360570651369 + ], + [ + 0.5022153449363472, + 0.0, + 0.46772220990755176 + ], + [ + 0.5614938253105886, + -0.182440403156569, + 0.15733605706513676 + ], + [ + 0.5614938253105886, + 0.182440403156569, + 0.15733605706513676 + ], + [ + 0.5903895464571245, + 0.0, + -0.1573360570651369 + ] + ], + "short_name": "J48" + }, + "Gyroelongated Pentagonal Cupola": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.7757682843725257, + 0.0 + ], + [ + 0.0, + 0.7757682843725257, + 0.0 + ], + [ + -0.7757682843725257, + 0.0, + -0.41347725003536473 + ], + [ + 0.40784552288992015, + 0.0, + 0.2520623953054439 + ], + [ + 0.12603119765272194, + -0.3878841421862628, + 0.2520623953054439 + ], + [ + 0.12603119765272194, + 0.3878841421862628, + 0.2520623953054439 + ], + [ + 0.7757682843725257, + 0.0, + -0.41347725003536473 + ], + [ + -0.45598515675040396, + -0.6276097257544702, + 0.0 + ], + [ + -0.45598515675040396, + 0.6276097257544702, + 0.0 + ], + [ + 0.45598515675040396, + -0.6276097257544702, + 0.0 + ], + [ + 0.45598515675040396, + 0.6276097257544702, + 0.0 + ], + [ + -0.32995395909768205, + -0.23972558356820736, + 0.2520623953054439 + ], + [ + -0.32995395909768205, + 0.23972558356820736, + 0.2520623953054439 + ], + [ + -0.23972558356820736, + -0.7377994819876021, + -0.41347725003536473 + ], + [ + -0.23972558356820736, + 0.7377994819876023, + -0.41347725003536473 + ], + [ + 0.23972558356820736, + -0.7377994819876021, + -0.41347725003536473 + ], + [ + 0.23972558356820736, + 0.7377994819876023, + -0.41347725003536473 + ], + [ + -0.6276097257544702, + -0.45598515675040396, + -0.41347725003536473 + ], + [ + -0.6276097257544702, + 0.45598515675040396, + -0.41347725003536473 + ], + [ + 0.6276097257544702, + -0.45598515675040396, + -0.41347725003536473 + ], + [ + 0.6276097257544702, + 0.45598515675040396, + -0.41347725003536473 + ], + [ + -0.7377994819876021, + -0.23972558356820736, + 0.0 + ], + [ + -0.7377994819876021, + 0.23972558356820736, + 0.0 + ], + [ + 0.7377994819876023, + -0.23972558356820736, + 0.0 + ], + [ + 0.7377994819876023, + 0.23972558356820736, + 0.0 + ] + ], + "short_name": "J24" + }, + "Gyroelongated Pentagonal Cupolarotunda": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.6422363687498056, + -0.17115299308617413 + ], + [ + 0.0, + 0.6422363687498056, + -0.17115299308617413 + ], + [ + 0.0, + -0.5463188862301009, + 0.5087966334723633 + ], + [ + 0.0, + 0.33764364038618927, + 0.7174718793162749 + ], + [ + -0.6422363687498056, + 0.0, + 0.17115299308617396 + ], + [ + 0.33764364038618927, + 0.0, + -0.37982823893008566 + ], + [ + -0.19846195234934533, + -0.6108030835012398, + 0.17115299308617396 + ], + [ + 0.10433762292195582, + -0.3211181843749028, + -0.37982823893008566 + ], + [ + 0.10433762292195582, + 0.3211181843749028, + -0.37982823893008566 + ], + [ + 0.6422363687498056, + 0.0, + 0.17115299308617396 + ], + [ + -0.3774970660370063, + -0.5195801367242481, + -0.17115299308617413 + ], + [ + -0.3774970660370063, + 0.5195801367242481, + -0.17115299308617413 + ], + [ + 0.3774970660370063, + -0.5195801367242481, + -0.17115299308617413 + ], + [ + 0.3774970660370063, + 0.5195801367242481, + -0.17115299308617413 + ], + [ + -0.27315944311505047, + -0.19846195234934533, + -0.37982823893008566 + ], + [ + -0.27315944311505047, + 0.19846195234934533, + -0.37982823893008566 + ], + [ + -0.19846195234934533, + 0.6108030835012398, + 0.17115299308617396 + ], + [ + 0.19846195234934533, + -0.6108030835012398, + 0.17115299308617396 + ], + [ + 0.19846195234934533, + 0.6108030835012398, + 0.17115299308617396 + ], + [ + -0.5195801367242481, + -0.3774970660370063, + 0.17115299308617396 + ], + [ + -0.5195801367242481, + 0.3774970660370063, + 0.17115299308617396 + ], + [ + 0.5195801367242481, + -0.3774970660370063, + 0.17115299308617396 + ], + [ + 0.5195801367242481, + 0.3774970660370063, + 0.17115299308617396 + ], + [ + -0.6108030835012398, + -0.19846195234934533, + -0.17115299308617413 + ], + [ + -0.6108030835012398, + 0.19846195234934533, + -0.17115299308617413 + ], + [ + 0.6108030835012398, + -0.19846195234934533, + -0.17115299308617413 + ], + [ + 0.6108030835012398, + 0.19846195234934533, + -0.17115299308617413 + ], + [ + 0.5195801367242481, + -0.16882182019309463, + 0.5087966334723633 + ], + [ + 0.3211181843749028, + 0.441981263308145, + 0.5087966334723633 + ], + [ + -0.3211181843749028, + 0.10433762292195582, + 0.7174718793162749 + ], + [ + -0.19846195234934533, + -0.27315944311505047, + 0.7174718793162749 + ], + [ + -0.5195801367242481, + -0.16882182019309463, + 0.5087966334723633 + ], + [ + -0.3211181843749028, + 0.441981263308145, + 0.5087966334723633 + ], + [ + 0.19846195234934533, + -0.27315944311505047, + 0.7174718793162749 + ], + [ + 0.3211181843749028, + 0.10433762292195582, + 0.7174718793162749 + ] + ], + "short_name": "J47" + }, + "Gyroelongated Pentagonal Pyramid": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + 0.0, + 0.7705584367968087 + ], + [ + -0.6892084181254557, + 0.0, + -0.3446042090627279 + ], + [ + 0.6892084181254557, + 0.0, + 0.3446042090627279 + ], + [ + -0.21297711386704038, + -0.6554761571436897, + -0.3446042090627279 + ], + [ + -0.21297711386704038, + 0.6554761571436897, + -0.3446042090627279 + ], + [ + 0.21297711386704038, + -0.6554761571436897, + 0.3446042090627279 + ], + [ + 0.21297711386704038, + 0.6554761571436897, + 0.3446042090627279 + ], + [ + -0.5575813229297684, + -0.40510654392996737, + 0.3446042090627279 + ], + [ + -0.5575813229297684, + 0.40510654392996737, + 0.3446042090627279 + ], + [ + 0.5575813229297684, + -0.40510654392996737, + -0.3446042090627279 + ], + [ + 0.5575813229297684, + 0.40510654392996737, + -0.3446042090627279 + ] + ], + "short_name": "J11" + }, + "Gyroelongated Pentagonal Rotunda": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.6767517231178509, + 0.0 + ], + [ + 0.0, + 0.6767517231178509, + 0.0 + ], + [ + -0.6767517231178509, + 0.0, + -0.36070234768336146 + ], + [ + 0.6767517231178509, + 0.0, + -0.36070234768336146 + ], + [ + -0.3977846823121919, + -0.5475036449748704, + 0.0 + ], + [ + -0.3977846823121919, + 0.5475036449748704, + 0.0 + ], + [ + 0.3977846823121919, + -0.5475036449748704, + 0.0 + ], + [ + 0.3977846823121919, + 0.5475036449748704, + 0.0 + ], + [ + -0.2091277834159449, + -0.6436291361852056, + -0.36070234768336146 + ], + [ + -0.2091277834159449, + 0.6436291361852057, + -0.36070234768336146 + ], + [ + 0.2091277834159449, + -0.6436291361852056, + -0.36070234768336146 + ], + [ + 0.2091277834159449, + 0.6436291361852057, + -0.36070234768336146 + ], + [ + -0.5475036449748704, + -0.3977846823121919, + -0.36070234768336146 + ], + [ + -0.5475036449748704, + 0.3977846823121919, + -0.36070234768336146 + ], + [ + 0.5475036449748704, + -0.3977846823121919, + -0.36070234768336146 + ], + [ + 0.5475036449748704, + 0.3977846823121919, + -0.36070234768336146 + ], + [ + -0.6436291361852056, + -0.2091277834159449, + 0.0 + ], + [ + -0.6436291361852056, + 0.2091277834159449, + 0.0 + ], + [ + 0.6436291361852057, + -0.2091277834159449, + 0.0 + ], + [ + 0.6436291361852057, + 0.2091277834159449, + 0.0 + ], + [ + 0.5756794003238358, + 0.0, + 0.3557894360232877 + ], + [ + 0.17789471801164386, + -0.5475036449748704, + 0.3557894360232877 + ], + [ + 0.17789471801164386, + 0.5475036449748704, + 0.3557894360232877 + ], + [ + -0.4657344181735617, + -0.33837586155892546, + 0.3557894360232877 + ], + [ + -0.4657344181735617, + 0.33837586155892546, + 0.3557894360232877 + ], + [ + -0.3557894360232877, + 0.0, + 0.5756794003238358 + ], + [ + -0.10994498215027401, + -0.33837586155892546, + 0.5756794003238358 + ], + [ + -0.10994498215027401, + 0.33837586155892546, + 0.5756794003238358 + ], + [ + 0.2878397001619179, + -0.2091277834159449, + 0.5756794003238358 + ], + [ + 0.2878397001619179, + 0.2091277834159449, + 0.5756794003238358 + ] + ], + "short_name": "J25" + }, + "Gyroelongated Square Bicupola": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.35131954773256, + -0.5650345470523362 + ], + [ + 0.0, + 0.35131954773256, + -0.5650345470523362 + ], + [ + 0.0, + -0.6491538790424686, + 0.21371499931977617 + ], + [ + 0.0, + 0.6491538790424686, + 0.21371499931977617 + ], + [ + -0.35131954773256, + 0.0, + -0.5650345470523362 + ], + [ + 0.35131954773256, + 0.0, + -0.5650345470523362 + ], + [ + -0.3245769395212343, + 0.1344441703832471, + 0.5650345470523362 + ], + [ + 0.3245769395212343, + -0.1344441703832471, + 0.5650345470523362 + ], + [ + 0.5997399822976442, + 0.2484204345650842, + -0.21371499931977617 + ], + [ + -0.6491538790424686, + 0.0, + 0.21371499931977617 + ], + [ + 0.6491538790424686, + 0.0, + 0.21371499931977617 + ], + [ + -0.45902110990448136, + -0.45902110990448136, + 0.21371499931977617 + ], + [ + -0.45902110990448136, + 0.45902110990448136, + 0.21371499931977617 + ], + [ + 0.45902110990448136, + -0.45902110990448136, + 0.21371499931977617 + ], + [ + 0.45902110990448136, + 0.45902110990448136, + 0.21371499931977617 + ], + [ + -0.2484204345650842, + -0.5997399822976442, + -0.21371499931977617 + ], + [ + 0.2484204345650842, + 0.5997399822976442, + -0.21371499931977617 + ], + [ + 0.2484204345650842, + -0.5997399822976442, + -0.21371499931977617 + ], + [ + -0.2484204345650842, + 0.5997399822976442, + -0.21371499931977617 + ], + [ + 0.5997399822976442, + -0.2484204345650842, + -0.21371499931977617 + ], + [ + -0.5997399822976442, + 0.2484204345650842, + -0.21371499931977617 + ], + [ + -0.5997399822976442, + -0.2484204345650842, + -0.21371499931977617 + ], + [ + -0.1344441703832471, + -0.3245769395212343, + 0.5650345470523362 + ], + [ + 0.1344441703832471, + 0.3245769395212343, + 0.5650345470523362 + ] + ], + "short_name": "J45" + }, + "Gyroelongated Square Cupola": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.3846832572638277, + 0.3846832572638277 + ], + [ + 0.0, + 0.3846832572638277, + 0.3846832572638277 + ], + [ + 0.0, + -0.7108019757716485, + -0.46802167767249886 + ], + [ + 0.0, + 0.7108019757716485, + -0.46802167767249886 + ], + [ + -0.3846832572638277, + 0.0, + 0.3846832572638277 + ], + [ + 0.3846832572638277, + 0.0, + 0.3846832572638277 + ], + [ + -0.6566953970840095, + -0.2720121398201818, + 0.0 + ], + [ + -0.7108019757716485, + 0.0, + -0.46802167767249886 + ], + [ + 0.7108019757716485, + 0.0, + -0.46802167767249886 + ], + [ + -0.5026128971489287, + -0.5026128971489287, + -0.46802167767249886 + ], + [ + -0.5026128971489287, + 0.5026128971489288, + -0.46802167767249886 + ], + [ + 0.5026128971489288, + -0.5026128971489287, + -0.46802167767249886 + ], + [ + 0.5026128971489288, + 0.5026128971489288, + -0.46802167767249886 + ], + [ + -0.2720121398201818, + -0.6566953970840095, + 0.0 + ], + [ + 0.2720121398201818, + 0.6566953970840095, + 0.0 + ], + [ + 0.2720121398201818, + -0.6566953970840095, + 0.0 + ], + [ + -0.2720121398201818, + 0.6566953970840095, + 0.0 + ], + [ + 0.6566953970840095, + -0.2720121398201818, + 0.0 + ], + [ + -0.6566953970840095, + 0.2720121398201818, + 0.0 + ], + [ + 0.6566953970840095, + 0.2720121398201818, + 0.0 + ] + ], + "short_name": "J23" + }, + "Gyroelongated Square Dipyramid": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.44396929387665046, + -0.44396929387665046, + -0.3733321877035983 + ], + [ + -0.44396929387665046, + 0.44396929387665046, + -0.3733321877035983 + ], + [ + 0.0, + 0.0, + -1.0011995843811636 + ], + [ + 0.0, + 0.0, + 1.0011995843811636 + ], + [ + 0.0, + -0.6278673966775653, + 0.3733321877035983 + ], + [ + 0.0, + 0.6278673966775653, + 0.3733321877035983 + ], + [ + 0.44396929387665046, + -0.44396929387665046, + -0.3733321877035983 + ], + [ + 0.44396929387665046, + 0.44396929387665046, + -0.3733321877035983 + ], + [ + -0.6278673966775653, + 0.0, + 0.3733321877035983 + ], + [ + 0.6278673966775653, + 0.0, + 0.3733321877035983 + ] + ], + "short_name": "J17" + }, + "Gyroelongated Square Pyramid": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.4714757127933015, + -0.4714757127933015, + -0.3964622367670771 + ], + [ + -0.4714757127933015, + 0.4714757127933015, + -0.3964622367670771 + ], + [ + 0.0, + 0.0, + 1.0632295841288861 + ], + [ + 0.0, + -0.6667673473618091, + 0.3964622367670771 + ], + [ + 0.0, + 0.6667673473618091, + 0.3964622367670771 + ], + [ + 0.4714757127933015, + -0.4714757127933015, + -0.3964622367670771 + ], + [ + 0.4714757127933015, + 0.4714757127933015, + -0.3964622367670771 + ], + [ + -0.6667673473618091, + 0.0, + 0.3964622367670771 + ], + [ + 0.6667673473618091, + 0.0, + 0.3964622367670771 + ] + ], + "short_name": "J10" + }, + "Gyroelongated Triangular Bicupola": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.5972207655339531, + 0.0, + 0.2554909470942446 + ], + [ + -0.29861038276697655, + -0.5172083546199933, + 0.2554909470942446 + ], + [ + -0.29861038276697655, + 0.5172083546199933, + 0.2554909470942446 + ], + [ + -0.29861038276697655, + -0.1724027848733311, + 0.7431196602117565 + ], + [ + 0.0, + -0.5972207655339531, + -0.2554909470942446 + ], + [ + 0.0, + 0.5972207655339531, + -0.2554909470942446 + ], + [ + 0.0, + 0.3448055697466622, + 0.7431196602117565 + ], + [ + 0.29861038276697655, + -0.1724027848733311, + 0.7431196602117565 + ], + [ + 0.29861038276697655, + -0.5172083546199933, + 0.2554909470942446 + ], + [ + 0.29861038276697655, + 0.5172083546199933, + 0.2554909470942446 + ], + [ + 0.5972207655339531, + 0.0, + 0.2554909470942446 + ], + [ + -0.3448055697466622, + 0.0, + -0.7431196602117565 + ], + [ + 0.1724027848733311, + -0.29861038276697655, + -0.7431196602117565 + ], + [ + 0.1724027848733311, + 0.29861038276697655, + -0.7431196602117565 + ], + [ + -0.5172083546199933, + -0.29861038276697655, + -0.2554909470942446 + ], + [ + -0.5172083546199933, + 0.29861038276697655, + -0.2554909470942446 + ], + [ + 0.5172083546199933, + -0.29861038276697655, + -0.2554909470942446 + ], + [ + 0.5172083546199933, + 0.29861038276697655, + -0.2554909470942446 + ] + ], + "short_name": "J44" + }, + "Gyroelongated Triangular Cupola": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.6576298614609687, + 0.0, + -0.5626678971616152 + ], + [ + -0.32881493073048434, + -0.5695241663124399, + -0.5626678971616152 + ], + [ + -0.32881493073048434, + 0.5695241663124399, + -0.5626678971616152 + ], + [ + 0.0, + -0.6576298614609687, + 0.0 + ], + [ + 0.0, + 0.6576298614609687, + 0.0 + ], + [ + 0.32881493073048434, + -0.5695241663124399, + -0.5626678971616152 + ], + [ + 0.32881493073048434, + 0.5695241663124399, + -0.5626678971616152 + ], + [ + 0.6576298614609687, + 0.0, + -0.5626678971616152 + ], + [ + -0.1898413887708133, + -0.32881493073048434, + 0.5369525333988551 + ], + [ + -0.1898413887708133, + 0.32881493073048434, + 0.5369525333988551 + ], + [ + 0.3796827775416266, + 0.0, + 0.5369525333988551 + ], + [ + -0.5695241663124399, + -0.32881493073048434, + 0.0 + ], + [ + -0.5695241663124399, + 0.32881493073048434, + 0.0 + ], + [ + 0.5695241663124399, + -0.32881493073048434, + 0.0 + ], + [ + 0.5695241663124399, + 0.32881493073048434, + 0.0 + ] + ], + "short_name": "J22" + }, + "Hebesphenomegacorona": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.35010176072230587, + -0.35010176072230587, + 0.6835429403477223 + ], + [ + -0.35010176072230587, + 0.0, + -0.5870772593435647 + ], + [ + -0.35010176072230587, + 0.35010176072230587, + 0.6835429403477223 + ], + [ + 0.0, + -0.7711313667945113, + 0.24713968715951026 + ], + [ + 0.0, + 0.7711313667945113, + 0.24713968715951026 + ], + [ + 0.0, + -0.585131424747188, + -0.42790771339974376 + ], + [ + 0.0, + 0.585131424747188, + -0.42790771339974376 + ], + [ + 0.35010176072230587, + -0.35010176072230587, + 0.6835429403477223 + ], + [ + 0.35010176072230587, + 0.0, + -0.5870772593435647 + ], + [ + 0.35010176072230587, + 0.35010176072230587, + 0.6835429403477223 + ], + [ + -0.501937264291919, + -0.35010176072230587, + 0.0 + ], + [ + -0.501937264291919, + 0.35010176072230587, + 0.0 + ], + [ + 0.501937264291919, + -0.35010176072230587, + 0.0 + ], + [ + 0.501937264291919, + 0.35010176072230587, + 0.0 + ] + ], + "short_name": "J89" + }, + "Metabiaugmented Dodecahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + 0.0, + 0.6930282779870623 + ], + [ + 0.0, + 0.0, + -0.6930282779870625 + ], + [ + 0.08823774900874909, + -0.6474078612750428, + 0.23100942599568747 + ], + [ + 0.08823774900874909, + 0.6474078612750428, + 0.23100942599568747 + ], + [ + 0.23100942599568747, + -0.40012006285185325, + -0.5165527799695642 + ], + [ + 0.23100942599568747, + 0.40012006285185325, + -0.5165527799695642 + ], + [ + 0.5165527799695642, + -0.40012006285185325, + 0.23100942599568747 + ], + [ + 0.5165527799695642, + 0.40012006285185325, + 0.23100942599568747 + ], + [ + -0.6047905289783133, + -0.2472877984231895, + 0.23100942599568747 + ], + [ + -0.6047905289783133, + 0.2472877984231895, + 0.23100942599568747 + ], + [ + 0.6047905289783133, + -0.2472877984231895, + -0.23100942599568744 + ], + [ + 0.6047905289783133, + 0.2472877984231895, + -0.23100942599568744 + ], + [ + -0.4620188519913749, + 0.0, + -0.5165527799695642 + ], + [ + -0.23100942599568744, + -0.40012006285185325, + 0.5165527799695642 + ], + [ + -0.23100942599568744, + 0.40012006285185325, + 0.5165527799695642 + ], + [ + 0.46201885199137493, + 0.0, + 0.5165527799695642 + ], + [ + -0.5165527799695642, + -0.40012006285185325, + -0.23100942599568744 + ], + [ + -0.5165527799695642, + 0.40012006285185325, + -0.23100942599568744 + ], + [ + -0.4921644659617024, + 0.0, + 0.6442516499713389 + ], + [ + -0.08823774900874909, + -0.6474078612750428, + -0.23100942599568744 + ], + [ + -0.08823774900874909, + 0.6474078612750428, + -0.23100942599568744 + ], + [ + 0.3981694169904876, + -0.6896496602476031, + -0.1520871840096364 + ] + ], + "short_name": "J60" + }, + "Metabiaugmented Hexagonal Prism": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.6880896564787737, + 0.0, + -0.34404482823938687 + ], + [ + -0.6880896564787737, + 0.0, + 0.34404482823938687 + ], + [ + -0.34404482823938687, + -0.5959031225919257, + -0.34404482823938687 + ], + [ + -0.34404482823938687, + -0.5959031225919257, + 0.34404482823938687 + ], + [ + -0.34404482823938687, + 0.5959031225919257, + -0.34404482823938687 + ], + [ + -0.34404482823938687, + 0.5959031225919257, + 0.34404482823938687 + ], + [ + 0.34404482823938687, + -0.5959031225919257, + -0.34404482823938687 + ], + [ + 0.34404482823938687, + -0.5959031225919257, + 0.34404482823938687 + ], + [ + 0.34404482823938687, + 0.5959031225919257, + -0.34404482823938687 + ], + [ + 0.34404482823938687, + 0.5959031225919257, + 0.34404482823938687 + ], + [ + 0.6880896564787737, + 0.0, + -0.34404482823938687 + ], + [ + 0.6880896564787737, + 0.0, + 0.34404482823938687 + ], + [ + -0.9374343812740695, + 0.5412279923761942, + 0.0 + ], + [ + 0.9374343812740695, + 0.5412279923761942, + 0.0 + ] + ], + "short_name": "J56" + }, + "Metabiaugmented Truncated Dodecahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.361473603750252, + -0.2924382884519096, + 0.4731750903270356 + ], + [ + -0.5848765769038192, + -0.2924382884519096, + -0.1117014865767836 + ], + [ + 0.5848765769038192, + 0.2924382884519096, + 0.1117014865767836 + ], + [ + -0.361473603750252, + 0.2924382884519096, + -0.4731750903270356 + ], + [ + -0.1117014865767836, + -0.5848765769038192, + 0.2924382884519096 + ], + [ + 0.2924382884519096, + 0.4731750903270356, + -0.361473603750252 + ], + [ + 0.2924382884519096, + -0.4731750903270356, + 0.361473603750252 + ], + [ + 0.5848765769038192, + 0.2924382884519096, + -0.1117014865767836 + ], + [ + -0.4731750903270356, + 0.361473603750252, + 0.2924382884519096 + ], + [ + -0.2924382884519096, + -0.1117014865767836, + 0.5848765769038192 + ], + [ + 0.0, + 0.6539118922021616, + 0.1117014865767836 + ], + [ + -0.361473603750252, + -0.2924382884519096, + 0.4731750903270356 + ], + [ + 0.0, + 0.6539118922021616, + -0.1117014865767836 + ], + [ + -0.5848765769038192, + -0.2924382884519096, + 0.1117014865767836 + ], + [ + -0.2924382884519096, + 0.4731750903270356, + -0.361473603750252 + ], + [ + 0.0, + -0.6539118922021616, + 0.1117014865767836 + ], + [ + 0.361473603750252, + 0.2924382884519096, + -0.4731750903270356 + ], + [ + 0.4731750903270356, + -0.361473603750252, + -0.2924382884519096 + ], + [ + -0.2924382884519096, + -0.4731750903270356, + -0.361473603750252 + ], + [ + -0.1117014865767836, + 0.0, + -0.6539118922021616 + ], + [ + 0.0, + -0.6539118922021616, + -0.1117014865767836 + ], + [ + 0.2924382884519096, + 0.1117014865767836, + -0.5848765769038192 + ], + [ + 0.5848765769038192, + -0.2924382884519096, + -0.1117014865767836 + ], + [ + -0.1117014865767836, + -0.5848765769038192, + -0.2924382884519096 + ], + [ + 0.1117014865767836, + 0.0, + -0.6539118922021616 + ], + [ + -0.2924382884519096, + 0.1117014865767836, + 0.5848765769038192 + ], + [ + -0.1117014865767836, + 0.5848765769038192, + 0.2924382884519096 + ], + [ + 0.1117014865767836, + -0.5848765769038192, + -0.2924382884519096 + ], + [ + 0.2924382884519096, + -0.1117014865767836, + -0.5848765769038192 + ], + [ + 0.2924382884519096, + -0.4731750903270356, + -0.361473603750252 + ], + [ + 0.361473603750252, + -0.2924382884519096, + -0.4731750903270356 + ], + [ + -0.361473603750252, + 0.2924382884519096, + 0.4731750903270356 + ], + [ + -0.2924382884519096, + 0.4731750903270356, + 0.361473603750252 + ], + [ + 0.4731750903270356, + -0.361473603750252, + 0.2924382884519096 + ], + [ + -0.4731750903270356, + -0.361473603750252, + -0.2924382884519096 + ], + [ + 0.6539118922021616, + 0.1117014865767836, + 0.0 + ], + [ + -0.2924382884519096, + 0.1117014865767836, + -0.5848765769038192 + ], + [ + 0.1117014865767836, + -0.5848765769038192, + 0.2924382884519096 + ], + [ + 0.4731750903270356, + 0.361473603750252, + -0.2924382884519096 + ], + [ + 0.2924382884519096, + -0.1117014865767836, + 0.5848765769038192 + ], + [ + -0.6539118922021616, + -0.1117014865767836, + 0.0 + ], + [ + 0.4731750903270356, + 0.361473603750252, + 0.2924382884519096 + ], + [ + -0.4731750903270356, + 0.361473603750252, + -0.2924382884519096 + ], + [ + 0.2924382884519096, + 0.1117014865767836, + 0.5848765769038192 + ], + [ + -0.6539118922021616, + 0.1117014865767836, + 0.0 + ], + [ + 0.361473603750252, + 0.2924382884519096, + 0.4731750903270356 + ], + [ + -0.5848765769038192, + 0.2924382884519096, + -0.1117014865767836 + ], + [ + 0.5848765769038192, + -0.2924382884519096, + 0.1117014865767836 + ], + [ + -0.361473603750252, + -0.2924382884519096, + -0.4731750903270356 + ], + [ + 0.6539118922021616, + -0.1117014865767836, + 0.0 + ], + [ + -0.2924382884519096, + -0.1117014865767836, + -0.5848765769038192 + ], + [ + -0.5848765769038192, + 0.2924382884519096, + 0.1117014865767836 + ], + [ + -0.1117014865767836, + 0.0, + 0.6539118922021616 + ], + [ + 0.1117014865767836, + 0.5848765769038192, + 0.2924382884519096 + ], + [ + -0.4731750903270356, + -0.361473603750252, + 0.2924382884519096 + ], + [ + -0.1117014865767836, + 0.5848765769038192, + -0.2924382884519096 + ], + [ + 0.1117014865767836, + 0.0, + 0.6539118922021616 + ], + [ + 0.2924382884519096, + 0.4731750903270356, + 0.361473603750252 + ], + [ + -0.2924382884519096, + -0.4731750903270356, + 0.361473603750252 + ], + [ + 0.1117014865767836, + 0.5848765769038192, + -0.2924382884519096 + ], + [ + 0.4922559821906843, + 0.1117014865767836, + 0.48496773003443183 + ], + [ + 0.4922559821906843, + -0.1117014865767836, + 0.48496773003443183 + ], + [ + 0.6039574687674679, + -0.180736801875126, + 0.30423092815930586 + ], + [ + 0.6729927840658103, + 0.0, + 0.19252944158252225 + ], + [ + 0.6039574687674679, + 0.180736801875126, + 0.30423092815930586 + ], + [ + -0.4922559821906843, + 0.1117014865767836, + 0.48496773003443183 + ], + [ + -0.4922559821906843, + -0.1117014865767836, + 0.48496773003443183 + ], + [ + -0.6039574687674679, + -0.180736801875126, + 0.30423092815930586 + ], + [ + -0.6729927840658103, + 0.0, + 0.19252944158252225 + ], + [ + -0.6039574687674679, + 0.180736801875126, + 0.30423092815930586 + ] + ], + "short_name": "J70" + }, + "Metabidiminished Icosahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.4294089712279723, + 0.0, + -0.6947983105209848 + ], + [ + -0.4294089712279723, + 0.0, + 0.6947983105209848 + ], + [ + 0.0, + -0.6947983105209848, + -0.4294089712279723 + ], + [ + 0.0, + 0.6947983105209848, + -0.4294089712279723 + ], + [ + 0.4294089712279723, + 0.0, + -0.6947983105209848 + ], + [ + 0.4294089712279723, + 0.0, + 0.6947983105209848 + ], + [ + -0.6947983105209848, + -0.4294089712279723, + 0.0 + ], + [ + -0.6947983105209848, + 0.4294089712279723, + 0.0 + ], + [ + 0.6947983105209848, + -0.4294089712279723, + 0.0 + ], + [ + 0.6947983105209848, + 0.4294089712279723, + 0.0 + ] + ], + "short_name": "J62" + }, + "Metabidiminished Rhombicosidodecahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.15009435383073877, + -0.15009435383073877, + -0.6358098858659154 + ], + [ + -0.15009435383073877, + -0.15009435383073877, + 0.6358098858659154 + ], + [ + -0.15009435383073877, + 0.15009435383073877, + -0.6358098858659154 + ], + [ + -0.15009435383073877, + 0.15009435383073877, + 0.6358098858659154 + ], + [ + -0.15009435383073877, + -0.6358098858659154, + -0.15009435383073877 + ], + [ + -0.15009435383073877, + 0.6358098858659154, + -0.15009435383073877 + ], + [ + 0.0, + -0.3929521198483272, + -0.5430464736790659 + ], + [ + 0.0, + 0.39295211984832706, + -0.5430464736790659 + ], + [ + 0.15009435383073877, + -0.15009435383073877, + -0.6358098858659154 + ], + [ + 0.15009435383073877, + -0.15009435383073877, + 0.6358098858659154 + ], + [ + 0.15009435383073877, + 0.15009435383073877, + -0.6358098858659154 + ], + [ + 0.15009435383073877, + 0.15009435383073877, + 0.6358098858659154 + ], + [ + 0.15009435383073877, + -0.6358098858659154, + -0.15009435383073877 + ], + [ + 0.15009435383073877, + 0.6358098858659154, + -0.15009435383073877 + ], + [ + -0.5430464736790659, + 0.0, + -0.3929521198483272 + ], + [ + -0.5430464736790659, + 0.0, + 0.39295211984832706 + ], + [ + -0.24285776601758832, + -0.48571553203517664, + -0.3929521198483272 + ], + [ + -0.24285776601758832, + 0.48571553203517664, + -0.3929521198483272 + ], + [ + -0.48571553203517664, + -0.3929521198483272, + -0.24285776601758832 + ], + [ + -0.48571553203517664, + -0.3929521198483272, + 0.24285776601758832 + ], + [ + -0.48571553203517664, + 0.39295211984832706, + -0.24285776601758832 + ], + [ + -0.48571553203517664, + 0.39295211984832706, + 0.24285776601758832 + ], + [ + -0.6358098858659154, + -0.15009435383073877, + -0.15009435383073877 + ], + [ + -0.6358098858659154, + -0.15009435383073877, + 0.15009435383073877 + ], + [ + -0.6358098858659154, + 0.15009435383073877, + -0.15009435383073877 + ], + [ + -0.6358098858659154, + 0.15009435383073877, + 0.15009435383073877 + ], + [ + -0.3929521198483272, + -0.5430464736790659, + 0.0 + ], + [ + -0.3929521198483272, + -0.24285776601758832, + -0.48571553203517664 + ], + [ + -0.3929521198483272, + -0.24285776601758832, + 0.48571553203517664 + ], + [ + -0.3929521198483272, + 0.24285776601758832, + -0.48571553203517664 + ], + [ + -0.3929521198483272, + 0.24285776601758832, + 0.48571553203517664 + ], + [ + -0.3929521198483272, + 0.5430464736790659, + 0.0 + ], + [ + 0.24285776601758832, + -0.48571553203517664, + -0.3929521198483272 + ], + [ + 0.24285776601758832, + 0.48571553203517664, + -0.3929521198483272 + ], + [ + 0.48571553203517664, + -0.3929521198483272, + -0.24285776601758832 + ], + [ + 0.48571553203517664, + -0.3929521198483272, + 0.24285776601758832 + ], + [ + 0.48571553203517664, + 0.39295211984832706, + -0.24285776601758832 + ], + [ + 0.48571553203517664, + 0.39295211984832706, + 0.24285776601758832 + ], + [ + 0.6358098858659154, + -0.15009435383073877, + -0.15009435383073877 + ], + [ + 0.6358098858659154, + -0.15009435383073877, + 0.15009435383073877 + ], + [ + 0.6358098858659154, + 0.15009435383073877, + -0.15009435383073877 + ], + [ + 0.6358098858659154, + 0.15009435383073877, + 0.15009435383073877 + ], + [ + 0.39295211984832706, + -0.5430464736790659, + 0.0 + ], + [ + 0.39295211984832706, + -0.24285776601758832, + -0.48571553203517664 + ], + [ + 0.39295211984832706, + -0.24285776601758832, + 0.48571553203517664 + ], + [ + 0.39295211984832706, + 0.24285776601758832, + -0.48571553203517664 + ], + [ + 0.39295211984832706, + 0.24285776601758832, + 0.48571553203517664 + ], + [ + 0.39295211984832706, + 0.5430464736790659, + 0.0 + ], + [ + 0.5430464736790659, + 0.0, + -0.3929521198483272 + ], + [ + 0.5430464736790659, + 0.0, + 0.39295211984832706 + ] + ], + "short_name": "J81" + }, + "Metabigyrate Rhombicosidodecahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.1442842451438814, + -0.1442842451438814, + -0.6111978705117256 + ], + [ + -0.1442842451438814, + -0.1442842451438814, + 0.6111978705117256 + ], + [ + -0.1442842451438814, + 0.1442842451438814, + -0.6111978705117256 + ], + [ + -0.1442842451438814, + 0.1442842451438814, + 0.6111978705117256 + ], + [ + -0.1442842451438814, + -0.6111978705117256, + -0.1442842451438814 + ], + [ + 0.0, + -0.6358445620069737, + 0.10440506059433699 + ], + [ + -0.1442842451438814, + 0.6111978705117256, + -0.1442842451438814 + ], + [ + -0.2334568126839221, + 0.546671994466933, + 0.24868930573821843 + ], + [ + 0.0, + -0.3777410578278036, + -0.5220253029716849 + ], + [ + -0.1442842451438814, + -0.4023877493230516, + 0.4821461184221405 + ], + [ + 0.0, + 0.3777410578278035, + -0.5220253029716849 + ], + [ + 0.1442842451438814, + 0.4023877493230516, + 0.4821461184221405 + ], + [ + 0.1442842451438814, + -0.1442842451438814, + -0.6111978705117256 + ], + [ + 0.1442842451438814, + -0.1442842451438814, + 0.6111978705117256 + ], + [ + 0.1442842451438814, + 0.1442842451438814, + -0.6111978705117256 + ], + [ + 0.1442842451438814, + 0.1442842451438814, + 0.6111978705117256 + ], + [ + 0.1442842451438814, + -0.6111978705117256, + -0.1442842451438814 + ], + [ + 0.2334568126839221, + -0.546671994466933, + 0.24868930573821843 + ], + [ + 0.1442842451438814, + 0.6111978705117256, + -0.1442842451438814 + ], + [ + 0.0, + 0.6358445620069737, + 0.10440506059433699 + ], + [ + -0.5220253029716849, + 0.0, + -0.3777410578278036 + ], + [ + -0.5220253029716849, + 0.0, + 0.3777410578278035 + ], + [ + -0.2334568126839221, + -0.4669136253678442, + -0.3777410578278036 + ], + [ + -0.2334568126839221, + -0.546671994466933, + 0.24868930573821843 + ], + [ + -0.2334568126839221, + 0.4669136253678442, + -0.3777410578278036 + ], + [ + -0.1442842451438814, + 0.4023877493230516, + 0.4821461184221405 + ], + [ + -0.4669136253678442, + -0.3777410578278036, + -0.2334568126839221 + ], + [ + -0.4669136253678442, + -0.3777410578278036, + 0.2334568126839221 + ], + [ + -0.4669136253678442, + 0.3777410578278035, + -0.2334568126839221 + ], + [ + -0.4669136253678442, + 0.3777410578278035, + 0.2334568126839221 + ], + [ + -0.6111978705117256, + -0.1442842451438814, + -0.1442842451438814 + ], + [ + -0.6111978705117256, + -0.1442842451438814, + 0.1442842451438814 + ], + [ + -0.6111978705117256, + 0.1442842451438814, + -0.1442842451438814 + ], + [ + -0.6111978705117256, + 0.1442842451438814, + 0.1442842451438814 + ], + [ + -0.3777410578278036, + -0.5220253029716849, + 0.0 + ], + [ + -0.3777410578278036, + -0.2334568126839221, + -0.4669136253678442 + ], + [ + -0.3777410578278036, + -0.2334568126839221, + 0.4669136253678442 + ], + [ + -0.3777410578278036, + 0.2334568126839221, + -0.4669136253678442 + ], + [ + -0.3777410578278036, + 0.2334568126839221, + 0.4669136253678442 + ], + [ + -0.3777410578278036, + 0.5220253029716849, + 0.0 + ], + [ + 0.2334568126839221, + -0.4669136253678442, + -0.3777410578278036 + ], + [ + 0.1442842451438814, + -0.4023877493230516, + 0.4821461184221405 + ], + [ + 0.2334568126839221, + 0.4669136253678442, + -0.3777410578278036 + ], + [ + 0.2334568126839221, + 0.546671994466933, + 0.24868930573821843 + ], + [ + 0.4669136253678442, + -0.3777410578278036, + -0.2334568126839221 + ], + [ + 0.4669136253678442, + -0.3777410578278036, + 0.2334568126839221 + ], + [ + 0.4669136253678442, + 0.3777410578278035, + -0.2334568126839221 + ], + [ + 0.4669136253678442, + 0.3777410578278035, + 0.2334568126839221 + ], + [ + 0.6111978705117256, + -0.1442842451438814, + -0.1442842451438814 + ], + [ + 0.6111978705117256, + -0.1442842451438814, + 0.1442842451438814 + ], + [ + 0.6111978705117256, + 0.1442842451438814, + -0.1442842451438814 + ], + [ + 0.6111978705117256, + 0.1442842451438814, + 0.1442842451438814 + ], + [ + 0.3777410578278035, + -0.5220253029716849, + 0.0 + ], + [ + 0.3777410578278035, + -0.2334568126839221, + -0.4669136253678442 + ], + [ + 0.3777410578278035, + -0.2334568126839221, + 0.4669136253678442 + ], + [ + 0.3777410578278035, + 0.2334568126839221, + -0.4669136253678442 + ], + [ + 0.3777410578278035, + 0.2334568126839221, + 0.4669136253678442 + ], + [ + 0.3777410578278035, + 0.5220253029716849, + 0.0 + ], + [ + 0.5220253029716849, + 0.0, + -0.3777410578278036 + ], + [ + 0.5220253029716849, + 0.0, + 0.3777410578278035 + ] + ], + "short_name": "J74" + }, + "Metagyrate Diminished Rhombicosidodecahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.20243094860089703, + -0.147074693143019, + 0.6072928458026912 + ], + [ + 0.0, + 0.47594370478073167, + -0.4526493618213717 + ], + [ + -0.07732174199065969, + -0.23797185239036583, + 0.6072928458026912 + ], + [ + -0.2797526905915567, + 0.38504654553338485, + -0.4526493618213717 + ], + [ + 0.508599899939683, + 0.23797185239036583, + 0.340748285584749 + ], + [ + 0.5299711038120314, + 0.38504654553338485, + -0.04778746461957764 + ], + [ + -0.6072928458026912, + -0.147074693143019, + 0.20243094860089703 + ], + [ + -0.6550803104222687, + 0.0, + -0.04778746461957764 + ], + [ + 0.508599899939683, + -0.23797185239036583, + 0.340748285584749 + ], + [ + 0.2797526905915567, + 0.38504654553338485, + -0.4526493618213717 + ], + [ + -0.2797526905915567, + -0.38504654553338485, + 0.4526493618213717 + ], + [ + -0.4526493618213717, + 0.147074693143019, + -0.4526493618213717 + ], + [ + 0.2797526905915567, + -0.38504654553338485, + 0.4526493618213717 + ], + [ + 0.0, + -0.47594370478073167, + 0.4526493618213717 + ], + [ + 0.6337091065499203, + 0.147074693143019, + 0.09052987236427434 + ], + [ + 0.6072928458026912, + 0.147074693143019, + -0.20243094860089703 + ], + [ + -0.5299711038120314, + -0.38504654553338485, + 0.04778746461957764 + ], + [ + -0.577758568431609, + -0.23797185239036583, + -0.20243094860089703 + ], + [ + -0.07732174199065969, + 0.23797185239036583, + 0.6072928458026912 + ], + [ + -0.20243094860089703, + 0.6230183979237507, + -0.04778746461957764 + ], + [ + 0.43127815794902336, + 0.0, + 0.49539176956606845 + ], + [ + 0.32754015521113433, + 0.5321212386764038, + -0.20243094860089703 + ], + [ + -0.4526493618213717, + -0.147074693143019, + 0.4526493618213717 + ], + [ + -0.577758568431609, + 0.23797185239036583, + -0.20243094860089703 + ], + [ + 0.2797526905915567, + 0.38504654553338485, + 0.4526493618213717 + ], + [ + 0.20243094860089703, + 0.6230183979237507, + 0.04778746461957764 + ], + [ + -0.4526493618213717, + 0.147074693143019, + 0.4526493618213717 + ], + [ + -0.5299711038120314, + 0.38504654553338485, + 0.04778746461957764 + ], + [ + 0.0, + 0.47594370478073167, + 0.4526493618213717 + ], + [ + -0.04778746461957764, + 0.6230183979237507, + 0.20243094860089703 + ], + [ + -0.2797526905915567, + 0.38504654553338485, + 0.4526493618213717 + ], + [ + -0.32754015521113433, + 0.5321212386764038, + 0.20243094860089703 + ], + [ + 0.40486189720179405, + 0.47594370478073167, + 0.20243094860089703 + ], + [ + 0.20243094860089703, + 0.147074693143019, + 0.6072928458026912 + ], + [ + 0.04778746461957764, + 0.6230183979237507, + -0.20243094860089703 + ], + [ + -0.25021841322047467, + 0.0, + 0.6072928458026912 + ], + [ + -0.40486189720179405, + 0.47594370478073167, + -0.20243094860089703 + ], + [ + -0.6072928458026912, + 0.147074693143019, + 0.20243094860089703 + ], + [ + 0.6337091065499203, + -0.147074693143019, + 0.09052987236427434 + ], + [ + 0.4526493618213717, + 0.147074693143019, + -0.4526493618213717 + ], + [ + -0.32754015521113433, + -0.5321212386764038, + 0.20243094860089703 + ], + [ + -0.4526493618213717, + -0.147074693143019, + -0.4526493618213717 + ], + [ + 0.5299711038120314, + -0.3850465455333849, + -0.04778746461957764 + ], + [ + 0.4526493618213717, + -0.147074693143019, + -0.4526493618213717 + ], + [ + -0.20243094860089703, + -0.6230183979237507, + -0.04778746461957764 + ], + [ + -0.2797526905915567, + -0.38504654553338485, + -0.4526493618213717 + ], + [ + 0.32754015521113433, + -0.5321212386764038, + -0.20243094860089703 + ], + [ + 0.2797526905915567, + -0.38504654553338485, + -0.4526493618213717 + ], + [ + 0.04778746461957764, + -0.6230183979237507, + -0.20243094860089703 + ], + [ + 0.0, + -0.47594370478073167, + -0.4526493618213717 + ], + [ + 0.6072928458026912, + -0.147074693143019, + -0.20243094860089703 + ], + [ + 0.40486189720179405, + -0.47594370478073167, + 0.20243094860089703 + ], + [ + -0.04778746461957764, + -0.6230183979237507, + 0.20243094860089703 + ], + [ + -0.40486189720179405, + -0.47594370478073167, + -0.20243094860089703 + ], + [ + 0.20243094860089703, + -0.6230183979237507, + 0.04778746461957764 + ] + ], + "short_name": "J78" + }, + "Parabiaugmented Dodecahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + 0.0, + 0.6930282779870623 + ], + [ + 0.0, + 0.0, + -0.6930282779870625 + ], + [ + 0.08823774900874909, + -0.6474078612750428, + 0.23100942599568747 + ], + [ + 0.08823774900874909, + 0.6474078612750428, + 0.23100942599568747 + ], + [ + 0.23100942599568747, + -0.40012006285185325, + -0.5165527799695642 + ], + [ + 0.23100942599568747, + 0.40012006285185325, + -0.5165527799695642 + ], + [ + 0.5165527799695642, + -0.40012006285185325, + 0.23100942599568747 + ], + [ + 0.5165527799695642, + 0.40012006285185325, + 0.23100942599568747 + ], + [ + -0.6047905289783133, + -0.2472877984231895, + 0.23100942599568747 + ], + [ + -0.6047905289783133, + 0.2472877984231895, + 0.23100942599568747 + ], + [ + 0.6047905289783133, + -0.2472877984231895, + -0.23100942599568744 + ], + [ + 0.6047905289783133, + 0.2472877984231895, + -0.23100942599568744 + ], + [ + -0.4620188519913749, + 0.0, + -0.5165527799695642 + ], + [ + -0.23100942599568744, + -0.40012006285185325, + 0.5165527799695642 + ], + [ + -0.23100942599568744, + 0.40012006285185325, + 0.5165527799695642 + ], + [ + 0.46201885199137493, + 0.0, + 0.5165527799695642 + ], + [ + -0.5165527799695642, + -0.40012006285185325, + -0.23100942599568744 + ], + [ + -0.5165527799695642, + 0.40012006285185325, + -0.23100942599568744 + ], + [ + 0.49216446596170244, + 0.0, + -0.6442516499713388 + ], + [ + -0.4921644659617024, + 0.0, + 0.6442516499713389 + ], + [ + -0.08823774900874909, + -0.6474078612750428, + -0.23100942599568744 + ], + [ + -0.08823774900874909, + 0.6474078612750428, + -0.23100942599568744 + ] + ], + "short_name": "J59" + }, + "Parabiaugmented Hexagonal Prism": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.6880896564787737, + 0.0, + -0.34404482823938687 + ], + [ + -0.6880896564787737, + 0.0, + 0.34404482823938687 + ], + [ + -0.34404482823938687, + -0.5959031225919257, + -0.34404482823938687 + ], + [ + -0.34404482823938687, + -0.5959031225919257, + 0.34404482823938687 + ], + [ + -0.34404482823938687, + 0.5959031225919257, + -0.34404482823938687 + ], + [ + -0.34404482823938687, + 0.5959031225919257, + 0.34404482823938687 + ], + [ + 0.34404482823938687, + -0.5959031225919257, + -0.34404482823938687 + ], + [ + 0.34404482823938687, + -0.5959031225919257, + 0.34404482823938687 + ], + [ + 0.34404482823938687, + 0.5959031225919257, + -0.34404482823938687 + ], + [ + 0.34404482823938687, + 0.5959031225919257, + 0.34404482823938687 + ], + [ + 0.6880896564787737, + 0.0, + -0.34404482823938687 + ], + [ + 0.6880896564787737, + 0.0, + 0.34404482823938687 + ], + [ + -0.9374343812740695, + -0.5412279923761943, + 0.0 + ], + [ + 0.9374343812740695, + 0.5412279923761942, + 0.0 + ] + ], + "short_name": "J55" + }, + "Parabiaugmented Truncated Dodecahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.3614736037502521, + 0.5562506796927809 + ], + [ + 0.0, + -0.3614736037502521, + -0.5562506796927809 + ], + [ + 0.0, + 0.3614736037502521, + 0.5562506796927809 + ], + [ + 0.0, + 0.3614736037502521, + -0.5562506796927809 + ], + [ + 0.09501895985066552, + -0.6539118922021617, + 0.05872494676337293 + ], + [ + 0.09501895985066552, + 0.6539118922021617, + 0.05872494676337293 + ], + [ + 0.15374390661403847, + -0.4731750903270357, + 0.4388007861660351 + ], + [ + 0.15374390661403847, + 0.4731750903270357, + 0.4388007861660351 + ], + [ + -0.6149756264561539, + 0.0, + -0.24876286646470397 + ], + [ + -0.4612317198421154, + -0.4731750903270357, + 0.05872494676337293 + ], + [ + -0.4612317198421154, + 0.4731750903270357, + 0.05872494676337293 + ], + [ + -0.30748781322807694, + -0.5848765769038193, + -0.05872494676337293 + ], + [ + -0.30748781322807694, + 0.5848765769038193, + -0.05872494676337293 + ], + [ + -0.15374390661403847, + -0.4731750903270357, + -0.4388007861660351 + ], + [ + -0.15374390661403847, + 0.4731750903270357, + -0.4388007861660351 + ], + [ + 0.30748781322807694, + -0.5848765769038193, + 0.05872494676337293 + ], + [ + 0.30748781322807694, + 0.5848765769038193, + 0.05872494676337293 + ], + [ + 0.6149756264561539, + 0.0, + 0.24876286646470397 + ], + [ + 0.40250677307874244, + -0.29243828845190967, + -0.4388007861660351 + ], + [ + 0.40250677307874244, + 0.29243828845190967, + -0.4388007861660351 + ], + [ + 0.4612317198421154, + -0.4731750903270357, + -0.05872494676337293 + ], + [ + 0.4612317198421154, + 0.4731750903270357, + -0.05872494676337293 + ], + [ + 0.49752573292940794, + 0.0, + 0.4388007861660351 + ], + [ + 0.49752573292940794, + -0.3614736037502521, + -0.24876286646470397 + ], + [ + 0.49752573292940794, + 0.3614736037502521, + -0.24876286646470397 + ], + [ + -0.5925446927800735, + -0.29243828845190967, + 0.05872494676337293 + ], + [ + -0.5925446927800735, + 0.29243828845190967, + 0.05872494676337293 + ], + [ + 0.5925446927800735, + -0.29243828845190967, + -0.05872494676337293 + ], + [ + 0.5925446927800735, + 0.29243828845190967, + -0.05872494676337293 + ], + [ + 0.6512696395434463, + -0.11170148657678362, + 0.05872494676337293 + ], + [ + 0.6512696395434463, + 0.11170148657678362, + 0.05872494676337293 + ], + [ + -0.6512696395434463, + -0.11170148657678362, + -0.05872494676337293 + ], + [ + -0.6512696395434463, + 0.11170148657678362, + -0.05872494676337293 + ], + [ + 0.21246885337741137, + -0.29243828845190967, + 0.5562506796927809 + ], + [ + 0.21246885337741137, + -0.29243828845190967, + -0.5562506796927809 + ], + [ + 0.21246885337741137, + 0.29243828845190967, + 0.5562506796927809 + ], + [ + 0.21246885337741137, + 0.29243828845190967, + -0.5562506796927809 + ], + [ + 0.19003791970133108, + -0.5848765769038193, + 0.24876286646470397 + ], + [ + 0.19003791970133108, + 0.5848765769038193, + 0.24876286646470397 + ], + [ + -0.21246885337741137, + -0.29243828845190967, + 0.5562506796927809 + ], + [ + -0.21246885337741137, + -0.29243828845190967, + -0.5562506796927809 + ], + [ + -0.21246885337741137, + 0.29243828845190967, + 0.5562506796927809 + ], + [ + -0.21246885337741137, + 0.29243828845190967, + -0.5562506796927809 + ], + [ + -0.3437818263153695, + -0.11170148657678362, + 0.5562506796927809 + ], + [ + -0.3437818263153695, + -0.11170148657678362, + -0.5562506796927809 + ], + [ + -0.3437818263153695, + 0.11170148657678362, + 0.5562506796927809 + ], + [ + -0.3437818263153695, + 0.11170148657678362, + -0.5562506796927809 + ], + [ + 0.3437818263153695, + -0.11170148657678362, + 0.5562506796927809 + ], + [ + 0.3437818263153695, + -0.11170148657678362, + -0.5562506796927809 + ], + [ + 0.3437818263153695, + 0.11170148657678362, + 0.5562506796927809 + ], + [ + 0.3437818263153695, + 0.11170148657678362, + -0.5562506796927809 + ], + [ + -0.49752573292940794, + 0.0, + -0.4388007861660351 + ], + [ + -0.49752573292940794, + -0.3614736037502521, + 0.24876286646470397 + ], + [ + -0.49752573292940794, + 0.3614736037502521, + 0.24876286646470397 + ], + [ + -0.19003791970133108, + -0.5848765769038193, + -0.24876286646470397 + ], + [ + -0.19003791970133108, + 0.5848765769038193, + -0.24876286646470397 + ], + [ + -0.40250677307874244, + -0.29243828845190967, + 0.4388007861660351 + ], + [ + -0.40250677307874244, + 0.29243828845190967, + 0.4388007861660351 + ], + [ + -0.09501895985066554, + -0.6539118922021617, + -0.05872494676337293 + ], + [ + -0.09501895985066554, + 0.6539118922021617, + -0.05872494676337293 + ], + [ + -0.05872494676337293, + 0.18073680187512606, + 0.6737005732195267 + ], + [ + -0.19003791970133108, + 0.0, + 0.6737005732195267 + ], + [ + -0.05872494676337293, + -0.18073680187512606, + 0.6737005732195267 + ], + [ + 0.15374390661403847, + -0.11170148657678362, + 0.6737005732195267 + ], + [ + 0.15374390661403847, + 0.11170148657678362, + 0.6737005732195267 + ], + [ + 0.05872494676337293, + 0.18073680187512606, + -0.6737005732195267 + ], + [ + -0.15374390661403847, + 0.11170148657678362, + -0.6737005732195267 + ], + [ + -0.15374390661403847, + -0.11170148657678362, + -0.6737005732195267 + ], + [ + 0.05872494676337293, + -0.18073680187512606, + -0.6737005732195267 + ], + [ + 0.19003791970133108, + 0.0, + -0.6737005732195267 + ] + ], + "short_name": "J69" + }, + "Parabidiminished Rhombicosidodecahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.48571553203517664, + 0.0, + -0.46194292180782215 + ], + [ + 0.39295211984832706, + 0.2854964265396691, + -0.46194292180782215 + ], + [ + 0.24285776601758832, + -0.5896208052230172, + 0.20658715497743207 + ], + [ + 0.39295211984832706, + -0.5408521933700592, + -0.048768611852958006 + ], + [ + -0.15009435383073877, + 0.6197614649322962, + 0.20658715497743207 + ], + [ + 0.0, + 0.6685300767852541, + -0.048768611852958006 + ], + [ + -0.15009435383073877, + -0.46194292180782215, + 0.46194292180782215 + ], + [ + 0.39295211984832706, + -0.2854964265396691, + -0.46194292180782215 + ], + [ + -0.39295211984832706, + 0.2854964265396691, + 0.46194292180782215 + ], + [ + 0.15009435383073877, + 0.46194292180782215, + -0.46194292180782215 + ], + [ + -0.39295211984832706, + -0.2854964265396691, + 0.46194292180782215 + ], + [ + -0.48571553203517664, + 0.0, + 0.46194292180782215 + ], + [ + 0.0, + -0.6685300767852541, + 0.048768611852958006 + ], + [ + 0.15009435383073877, + -0.6197614649322962, + -0.20658715497743207 + ], + [ + -0.39295211984832706, + 0.5408521933700592, + 0.048768611852958006 + ], + [ + -0.24285776601758832, + 0.5896208052230172, + -0.20658715497743207 + ], + [ + 0.6358098858659154, + 0.20658715497743207, + -0.048768611852958006 + ], + [ + 0.15009435383073877, + -0.46194292180782215, + 0.46194292180782215 + ], + [ + 0.5430464736790659, + -0.33426503839262706, + -0.20658715497743207 + ], + [ + -0.15009435383073877, + 0.46194292180782215, + 0.46194292180782215 + ], + [ + 0.24285776601758832, + 0.5896208052230172, + -0.20658715497743207 + ], + [ + 0.39295211984832706, + -0.2854964265396691, + 0.46194292180782215 + ], + [ + 0.6358098858659154, + -0.20658715497743207, + 0.048768611852958006 + ], + [ + 0.15009435383073877, + 0.46194292180782215, + 0.46194292180782215 + ], + [ + 0.39295211984832706, + 0.5408521933700592, + 0.048768611852958006 + ], + [ + 0.48571553203517664, + 0.0, + 0.46194292180782215 + ], + [ + 0.6358098858659154, + 0.048768611852958006, + 0.20658715497743207 + ], + [ + 0.39295211984832706, + 0.2854964265396691, + 0.46194292180782215 + ], + [ + 0.5430464736790659, + 0.33426503839262706, + 0.20658715497743207 + ], + [ + 0.48571553203517664, + -0.41317430995486415, + 0.20658715497743207 + ], + [ + 0.6358098858659154, + -0.048768611852958006, + -0.20658715497743207 + ], + [ + 0.48571553203517664, + 0.41317430995486415, + -0.20658715497743207 + ], + [ + 0.15009435383073877, + 0.6197614649322962, + 0.20658715497743207 + ], + [ + -0.24285776601758832, + -0.5896208052230172, + 0.20658715497743207 + ], + [ + 0.15009435383073877, + -0.46194292180782215, + -0.46194292180782215 + ], + [ + -0.5430464736790659, + 0.33426503839262706, + 0.20658715497743207 + ], + [ + -0.15009435383073877, + 0.46194292180782215, + -0.46194292180782215 + ], + [ + -0.3929521198483272, + -0.5408521933700592, + -0.048768611852958006 + ], + [ + -0.15009435383073877, + -0.46194292180782215, + -0.46194292180782215 + ], + [ + -0.6358098858659154, + 0.20658715497743207, + -0.048768611852958006 + ], + [ + -0.39295211984832706, + 0.2854964265396691, + -0.46194292180782215 + ], + [ + -0.5430464736790659, + -0.33426503839262706, + -0.20658715497743207 + ], + [ + -0.39295211984832706, + -0.2854964265396691, + -0.46194292180782215 + ], + [ + -0.6358098858659154, + -0.048768611852958006, + -0.20658715497743207 + ], + [ + -0.48571553203517664, + 0.0, + -0.46194292180782215 + ], + [ + -0.15009435383073877, + -0.6197614649322962, + -0.20658715497743207 + ], + [ + -0.48571553203517664, + -0.41317430995486415, + 0.20658715497743207 + ], + [ + -0.6358098858659154, + 0.048768611852958006, + 0.20658715497743207 + ], + [ + -0.48571553203517664, + 0.41317430995486415, + -0.20658715497743207 + ], + [ + -0.6358098858659154, + -0.20658715497743207, + 0.048768611852958006 + ] + ], + "short_name": "J80" + }, + "Parabigyrate Rhombicosidodecahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.24547101952821324, + 0.5957706792746074 + ], + [ + 0.4669136253678442, + 0.0, + -0.44406124595308233 + ], + [ + -0.2334568126839221, + -0.07585471666076248, + 0.5957706792746074 + ], + [ + 0.3777410578278035, + 0.27444494308563155, + -0.44406124595308233 + ], + [ + 0.2334568126839221, + -0.5667967557171889, + 0.1985902264248691 + ], + [ + 0.3777410578278035, + -0.5199159626138448, + -0.04688079310334414 + ], + [ + -0.1442842451438814, + 0.5957706792746074, + 0.1985902264248691 + ], + [ + 0.0, + 0.6426514723779514, + -0.04688079310334414 + ], + [ + -0.1442842451438814, + -0.44406124595308233, + 0.44406124595308233 + ], + [ + 0.3777410578278035, + -0.27444494308563155, + -0.44406124595308233 + ], + [ + -0.3777410578278035, + 0.27444494308563155, + 0.44406124595308233 + ], + [ + 0.1442842451438814, + 0.44406124595308233, + -0.44406124595308233 + ], + [ + -0.3777410578278035, + -0.27444494308563155, + 0.44406124595308233 + ], + [ + 0.1442842451438814, + -0.1985902264248691, + -0.5957706792746074 + ], + [ + -0.4669136253678442, + 0.0, + 0.44406124595308233 + ], + [ + 0.2334568126839221, + 0.07585471666076248, + -0.5957706792746074 + ], + [ + 0.0, + -0.6426514723779514, + 0.04688079310334414 + ], + [ + 0.1442842451438814, + -0.5957706792746074, + -0.1985902264248691 + ], + [ + -0.3777410578278035, + 0.5199159626138448, + 0.04688079310334414 + ], + [ + -0.2334568126839221, + 0.5667967557171889, + -0.1985902264248691 + ], + [ + 0.1442842451438814, + 0.1985902264248691, + 0.5957706792746074 + ], + [ + 0.6111978705117256, + 0.1985902264248691, + -0.04688079310334414 + ], + [ + 0.1442842451438814, + -0.44406124595308233, + 0.44406124595308233 + ], + [ + 0.5220253029716849, + -0.3213257361889757, + -0.1985902264248691 + ], + [ + -0.1442842451438814, + 0.44406124595308233, + 0.44406124595308233 + ], + [ + 0.2334568126839221, + 0.5667967557171889, + -0.1985902264248691 + ], + [ + 0.3777410578278035, + -0.27444494308563155, + 0.44406124595308233 + ], + [ + 0.6111978705117256, + -0.1985902264248691, + 0.04688079310334414 + ], + [ + 0.1442842451438814, + 0.44406124595308233, + 0.44406124595308233 + ], + [ + 0.3777410578278035, + 0.5199159626138448, + 0.04688079310334414 + ], + [ + 0.4669136253678442, + 0.0, + 0.44406124595308233 + ], + [ + 0.6111978705117256, + 0.04688079310334414, + 0.1985902264248691 + ], + [ + 0.3777410578278035, + 0.27444494308563155, + 0.44406124595308233 + ], + [ + 0.5220253029716849, + 0.3213257361889757, + 0.1985902264248691 + ], + [ + 0.4669136253678442, + -0.3971804528497382, + 0.1985902264248691 + ], + [ + 0.2334568126839221, + -0.07585471666076248, + 0.5957706792746074 + ], + [ + 0.6111978705117256, + -0.04688079310334414, + -0.1985902264248691 + ], + [ + -0.1442842451438814, + 0.1985902264248691, + 0.5957706792746074 + ], + [ + 0.4669136253678442, + 0.3971804528497382, + -0.1985902264248691 + ], + [ + 0.1442842451438814, + 0.5957706792746074, + 0.1985902264248691 + ], + [ + -0.2334568126839221, + -0.5667967557171889, + 0.1985902264248691 + ], + [ + 0.1442842451438814, + -0.44406124595308233, + -0.44406124595308233 + ], + [ + -0.5220253029716849, + 0.3213257361889757, + 0.1985902264248691 + ], + [ + -0.1442842451438814, + 0.44406124595308233, + -0.44406124595308233 + ], + [ + -0.3777410578278036, + -0.5199159626138448, + -0.04688079310334414 + ], + [ + -0.1442842451438814, + -0.44406124595308233, + -0.44406124595308233 + ], + [ + -0.6111978705117256, + 0.1985902264248691, + -0.04688079310334414 + ], + [ + -0.3777410578278035, + 0.27444494308563155, + -0.44406124595308233 + ], + [ + -0.5220253029716849, + -0.3213257361889757, + -0.1985902264248691 + ], + [ + -0.3777410578278035, + -0.27444494308563155, + -0.44406124595308233 + ], + [ + -0.6111978705117256, + -0.04688079310334414, + -0.1985902264248691 + ], + [ + -0.4669136253678442, + 0.0, + -0.44406124595308233 + ], + [ + -0.1442842451438814, + -0.5957706792746074, + -0.1985902264248691 + ], + [ + -0.4669136253678442, + -0.3971804528497382, + 0.1985902264248691 + ], + [ + -0.1442842451438814, + -0.1985902264248691, + -0.5957706792746074 + ], + [ + -0.6111978705117256, + 0.04688079310334414, + 0.1985902264248691 + ], + [ + 0.0, + 0.24547101952821324, + -0.5957706792746074 + ], + [ + -0.4669136253678442, + 0.3971804528497382, + -0.1985902264248691 + ], + [ + -0.6111978705117256, + -0.1985902264248691, + 0.04688079310334414 + ], + [ + -0.2334568126839221, + 0.07585471666076248, + -0.5957706792746074 + ] + ], + "short_name": "J73" + }, + "Paragyrate Diminished Rhombicosidodecahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.25021841322047467, + 0.6072928458026912 + ], + [ + 0.47594370478073167, + 0.0, + -0.4526493618213717 + ], + [ + -0.23797185239036583, + -0.07732174199065969, + 0.6072928458026912 + ], + [ + 0.38504654553338485, + 0.2797526905915567, + -0.4526493618213717 + ], + [ + 0.23797185239036583, + -0.577758568431609, + 0.20243094860089703 + ], + [ + 0.38504654553338485, + -0.5299711038120314, + -0.04778746461957764 + ], + [ + -0.147074693143019, + 0.6072928458026912, + 0.20243094860089703 + ], + [ + 0.0, + 0.6550803104222687, + -0.04778746461957764 + ], + [ + -0.147074693143019, + -0.4526493618213717, + 0.4526493618213717 + ], + [ + 0.38504654553338485, + -0.2797526905915567, + -0.4526493618213717 + ], + [ + -0.38504654553338485, + 0.2797526905915567, + 0.4526493618213717 + ], + [ + 0.147074693143019, + 0.4526493618213717, + -0.4526493618213717 + ], + [ + -0.38504654553338485, + -0.2797526905915567, + 0.4526493618213717 + ], + [ + -0.47594370478073167, + 0.0, + 0.4526493618213717 + ], + [ + 0.0, + -0.6550803104222687, + 0.04778746461957764 + ], + [ + 0.147074693143019, + -0.6072928458026912, + -0.20243094860089703 + ], + [ + -0.38504654553338485, + 0.5299711038120314, + 0.04778746461957764 + ], + [ + -0.23797185239036583, + 0.577758568431609, + -0.20243094860089703 + ], + [ + 0.147074693143019, + 0.20243094860089703, + 0.6072928458026912 + ], + [ + 0.6230183979237507, + 0.20243094860089703, + -0.04778746461957764 + ], + [ + 0.147074693143019, + -0.4526493618213717, + 0.4526493618213717 + ], + [ + 0.5321212386764038, + -0.32754015521113433, + -0.20243094860089703 + ], + [ + -0.147074693143019, + 0.4526493618213717, + 0.4526493618213717 + ], + [ + 0.23797185239036583, + 0.577758568431609, + -0.20243094860089703 + ], + [ + 0.38504654553338485, + -0.2797526905915567, + 0.4526493618213717 + ], + [ + 0.6230183979237507, + -0.20243094860089703, + 0.04778746461957764 + ], + [ + 0.147074693143019, + 0.4526493618213717, + 0.4526493618213717 + ], + [ + 0.38504654553338485, + 0.5299711038120314, + 0.04778746461957764 + ], + [ + 0.47594370478073167, + 0.0, + 0.4526493618213717 + ], + [ + 0.6230183979237507, + 0.04778746461957764, + 0.20243094860089703 + ], + [ + 0.38504654553338485, + 0.2797526905915567, + 0.4526493618213717 + ], + [ + 0.5321212386764038, + 0.32754015521113433, + 0.20243094860089703 + ], + [ + 0.47594370478073167, + -0.40486189720179405, + 0.20243094860089703 + ], + [ + 0.23797185239036583, + -0.07732174199065969, + 0.6072928458026912 + ], + [ + 0.6230183979237507, + -0.04778746461957764, + -0.20243094860089703 + ], + [ + -0.147074693143019, + 0.20243094860089703, + 0.6072928458026912 + ], + [ + 0.47594370478073167, + 0.40486189720179405, + -0.20243094860089703 + ], + [ + 0.147074693143019, + 0.6072928458026912, + 0.20243094860089703 + ], + [ + -0.23797185239036583, + -0.577758568431609, + 0.20243094860089703 + ], + [ + 0.147074693143019, + -0.4526493618213717, + -0.4526493618213717 + ], + [ + -0.5321212386764038, + 0.32754015521113433, + 0.20243094860089703 + ], + [ + -0.147074693143019, + 0.4526493618213717, + -0.4526493618213717 + ], + [ + -0.3850465455333849, + -0.5299711038120314, + -0.04778746461957764 + ], + [ + -0.147074693143019, + -0.4526493618213717, + -0.4526493618213717 + ], + [ + -0.6230183979237507, + 0.20243094860089703, + -0.04778746461957764 + ], + [ + -0.38504654553338485, + 0.2797526905915567, + -0.4526493618213717 + ], + [ + -0.5321212386764038, + -0.32754015521113433, + -0.20243094860089703 + ], + [ + -0.38504654553338485, + -0.2797526905915567, + -0.4526493618213717 + ], + [ + -0.6230183979237507, + -0.04778746461957764, + -0.20243094860089703 + ], + [ + -0.47594370478073167, + 0.0, + -0.4526493618213717 + ], + [ + -0.147074693143019, + -0.6072928458026912, + -0.20243094860089703 + ], + [ + -0.47594370478073167, + -0.40486189720179405, + 0.20243094860089703 + ], + [ + -0.6230183979237507, + 0.04778746461957764, + 0.20243094860089703 + ], + [ + -0.47594370478073167, + 0.40486189720179405, + -0.20243094860089703 + ], + [ + -0.6230183979237507, + -0.20243094860089703, + 0.04778746461957764 + ] + ], + "short_name": "J77" + }, + "Pentagonal Cupola": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -1.2215355466105815, + 0.0 + ], + [ + 0.0, + 1.2215355466105815, + 0.0 + ], + [ + 0.6421992414126347, + 0.0, + 0.3969009587424073 + ], + [ + 0.19845047937120364, + -0.6107677733052908, + 0.3969009587424073 + ], + [ + 0.19845047937120364, + 0.6107677733052908, + 0.3969009587424073 + ], + [ + -0.7180005794487246, + -0.9882430164410511, + 0.0 + ], + [ + -0.7180005794487246, + 0.9882430164410511, + 0.0 + ], + [ + 0.7180005794487246, + -0.9882430164410511, + 0.0 + ], + [ + 0.7180005794487246, + 0.9882430164410511, + 0.0 + ], + [ + -0.519550100077521, + -0.37747524313576036, + 0.3969009587424073 + ], + [ + -0.519550100077521, + 0.37747524313576036, + 0.3969009587424073 + ], + [ + -1.1617493414901559, + -0.37747524313576036, + 0.0 + ], + [ + -1.1617493414901559, + 0.37747524313576036, + 0.0 + ], + [ + 1.1617493414901559, + -0.37747524313576036, + 0.0 + ], + [ + 1.1617493414901559, + 0.37747524313576036, + 0.0 + ] + ], + "short_name": "J05" + }, + "Pentagonal Gyrobicupola": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.9695334058530934, + 0.0 + ], + [ + 0.0, + 0.9695334058530934, + 0.0 + ], + [ + -0.4123671877066202, + -0.299602299022829, + 0.31502049971744217 + ], + [ + -0.4123671877066202, + 0.299602299022829, + 0.31502049971744217 + ], + [ + 0.4123671877066202, + -0.299602299022829, + -0.31502049971744217 + ], + [ + 0.4123671877066202, + 0.299602299022829, + -0.31502049971744217 + ], + [ + -0.5097138756957981, + 0.0, + -0.31502049971744217 + ], + [ + 0.5097138756957981, + 0.0, + 0.31502049971744217 + ], + [ + -0.15751024985872109, + -0.4847667029265467, + -0.31502049971744217 + ], + [ + -0.15751024985872109, + 0.4847667029265467, + -0.31502049971744217 + ], + [ + 0.15751024985872109, + -0.4847667029265467, + 0.31502049971744217 + ], + [ + 0.15751024985872109, + 0.4847667029265467, + 0.31502049971744217 + ], + [ + -0.5698774375653413, + -0.7843690019493756, + 0.0 + ], + [ + -0.5698774375653413, + 0.7843690019493756, + 0.0 + ], + [ + 0.5698774375653413, + -0.7843690019493756, + 0.0 + ], + [ + 0.5698774375653413, + 0.7843690019493756, + 0.0 + ], + [ + -0.9220810634024184, + -0.299602299022829, + 0.0 + ], + [ + -0.9220810634024184, + 0.299602299022829, + 0.0 + ], + [ + 0.9220810634024184, + -0.299602299022829, + 0.0 + ], + [ + 0.9220810634024184, + 0.299602299022829, + 0.0 + ] + ], + "short_name": "J31" + }, + "Pentagonal Gyrocupolarotunda": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.7710253465099329, + 0.0 + ], + [ + 0.0, + 0.7710253465099329, + 0.0 + ], + [ + 0.4053520128927074, + 0.0, + -0.25052132137587874 + ], + [ + 0.12526066068793937, + -0.38551267325496646, + -0.25052132137587874 + ], + [ + 0.12526066068793937, + 0.38551267325496646, + -0.25052132137587874 + ], + [ + -0.45319732782223243, + -0.6237726084203683, + 0.0 + ], + [ + -0.45319732782223243, + 0.6237726084203683, + 0.0 + ], + [ + 0.45319732782223243, + -0.6237726084203683, + 0.0 + ], + [ + 0.45319732782223243, + 0.6237726084203683, + 0.0 + ], + [ + -0.3279366671342931, + -0.23825993516540184, + -0.25052132137587874 + ], + [ + -0.3279366671342931, + 0.23825993516540184, + -0.25052132137587874 + ], + [ + -0.7332886800270005, + -0.23825993516540184, + 0.0 + ], + [ + -0.7332886800270005, + 0.23825993516540184, + 0.0 + ], + [ + 0.7332886800270005, + -0.23825993516540184, + 0.0 + ], + [ + 0.7332886800270005, + 0.23825993516540184, + 0.0 + ], + [ + 0.6558733342685862, + 0.0, + 0.4053520128927074 + ], + [ + 0.2026760064463537, + -0.6237726084203683, + 0.4053520128927074 + ], + [ + 0.2026760064463537, + 0.6237726084203683, + 0.4053520128927074 + ], + [ + -0.5306126735806467, + -0.38551267325496646, + 0.4053520128927074 + ], + [ + -0.5306126735806467, + 0.38551267325496646, + 0.4053520128927074 + ], + [ + -0.4053520128927074, + 0.0, + 0.6558733342685862 + ], + [ + -0.12526066068793937, + -0.38551267325496646, + 0.6558733342685862 + ], + [ + -0.12526066068793937, + 0.38551267325496646, + 0.6558733342685862 + ], + [ + 0.3279366671342931, + -0.23825993516540184, + 0.6558733342685862 + ], + [ + 0.3279366671342931, + 0.23825993516540184, + 0.6558733342685862 + ] + ], + "short_name": "J33" + }, + "Pentagonal Orthobicupola": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.9695334058530934, + 0.0 + ], + [ + 0.0, + 0.9695334058530934, + 0.0 + ], + [ + 0.5097138756957981, + 0.0, + -0.31502049971744217 + ], + [ + 0.5097138756957981, + 0.0, + 0.31502049971744217 + ], + [ + 0.15751024985872109, + -0.4847667029265467, + -0.31502049971744217 + ], + [ + 0.15751024985872109, + -0.4847667029265467, + 0.31502049971744217 + ], + [ + 0.15751024985872109, + 0.4847667029265467, + -0.31502049971744217 + ], + [ + 0.15751024985872109, + 0.4847667029265467, + 0.31502049971744217 + ], + [ + -0.5698774375653413, + -0.7843690019493756, + 0.0 + ], + [ + -0.5698774375653413, + 0.7843690019493756, + 0.0 + ], + [ + 0.5698774375653413, + -0.7843690019493756, + 0.0 + ], + [ + 0.5698774375653413, + 0.7843690019493756, + 0.0 + ], + [ + -0.4123671877066202, + -0.299602299022829, + -0.31502049971744217 + ], + [ + -0.4123671877066202, + -0.299602299022829, + 0.31502049971744217 + ], + [ + -0.4123671877066202, + 0.299602299022829, + -0.31502049971744217 + ], + [ + -0.4123671877066202, + 0.299602299022829, + 0.31502049971744217 + ], + [ + -0.9220810634024184, + -0.299602299022829, + 0.0 + ], + [ + -0.9220810634024184, + 0.299602299022829, + 0.0 + ], + [ + 0.9220810634024184, + -0.299602299022829, + 0.0 + ], + [ + 0.9220810634024184, + 0.299602299022829, + 0.0 + ] + ], + "short_name": "J30" + }, + "Pentagonal Orthobirotunda": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.6739935637720124, + 0.0 + ], + [ + 0.0, + 0.6739935637720124, + 0.0 + ], + [ + -0.3961634769252353, + -0.5452722471908928, + 0.0 + ], + [ + -0.3961634769252353, + 0.5452722471908928, + 0.0 + ], + [ + 0.3961634769252353, + -0.5452722471908928, + 0.0 + ], + [ + 0.3961634769252353, + 0.5452722471908928, + 0.0 + ], + [ + -0.6410059707663655, + -0.2082754653048867, + 0.0 + ], + [ + -0.6410059707663655, + 0.2082754653048867, + 0.0 + ], + [ + 0.6410059707663655, + -0.2082754653048867, + 0.0 + ], + [ + 0.6410059707663655, + 0.2082754653048867, + 0.0 + ], + [ + 0.5733331698467344, + 0.0, + -0.3543393858429982 + ], + [ + 0.5733331698467344, + 0.0, + 0.3543393858429982 + ], + [ + 0.1771696929214991, + -0.5452722471908928, + -0.3543393858429982 + ], + [ + 0.1771696929214991, + -0.5452722471908928, + 0.3543393858429982 + ], + [ + 0.1771696929214991, + 0.5452722471908928, + -0.3543393858429982 + ], + [ + 0.1771696929214991, + 0.5452722471908928, + 0.3543393858429982 + ], + [ + -0.4638362778448663, + -0.3369967818860062, + -0.3543393858429982 + ], + [ + -0.4638362778448663, + -0.3369967818860062, + 0.3543393858429982 + ], + [ + -0.4638362778448663, + 0.3369967818860062, + -0.3543393858429982 + ], + [ + -0.4638362778448663, + 0.3369967818860062, + 0.3543393858429982 + ], + [ + -0.3543393858429982, + 0.0, + -0.5733331698467344 + ], + [ + -0.3543393858429982, + 0.0, + 0.5733331698467344 + ], + [ + -0.1094968920018681, + -0.3369967818860062, + -0.5733331698467344 + ], + [ + -0.1094968920018681, + -0.3369967818860062, + 0.5733331698467344 + ], + [ + -0.1094968920018681, + 0.3369967818860062, + -0.5733331698467344 + ], + [ + -0.1094968920018681, + 0.3369967818860062, + 0.5733331698467344 + ], + [ + 0.2866665849233672, + -0.2082754653048867, + -0.5733331698467344 + ], + [ + 0.2866665849233672, + -0.2082754653048867, + 0.5733331698467344 + ], + [ + 0.2866665849233672, + 0.2082754653048867, + -0.5733331698467344 + ], + [ + 0.2866665849233672, + 0.2082754653048867, + 0.5733331698467344 + ] + ], + "short_name": "J34" + }, + "Pentagonal Orthocupolarotunda": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.7710253465099329, + 0.0 + ], + [ + 0.0, + 0.7710253465099329, + 0.0 + ], + [ + 0.2026760064463537, + -0.6237726084203683, + 0.4053520128927074 + ], + [ + 0.2026760064463537, + 0.6237726084203683, + 0.4053520128927074 + ], + [ + 0.3279366671342931, + -0.23825993516540184, + -0.25052132137587874 + ], + [ + 0.3279366671342931, + -0.23825993516540184, + 0.6558733342685862 + ], + [ + 0.3279366671342931, + 0.23825993516540184, + -0.25052132137587874 + ], + [ + 0.3279366671342931, + 0.23825993516540184, + 0.6558733342685862 + ], + [ + -0.4053520128927074, + 0.0, + -0.25052132137587874 + ], + [ + -0.4053520128927074, + 0.0, + 0.6558733342685862 + ], + [ + -0.5306126735806467, + -0.38551267325496646, + 0.4053520128927074 + ], + [ + -0.5306126735806467, + 0.38551267325496646, + 0.4053520128927074 + ], + [ + -0.12526066068793937, + -0.38551267325496646, + -0.25052132137587874 + ], + [ + -0.12526066068793937, + -0.38551267325496646, + 0.6558733342685862 + ], + [ + -0.12526066068793937, + 0.38551267325496646, + -0.25052132137587874 + ], + [ + -0.12526066068793937, + 0.38551267325496646, + 0.6558733342685862 + ], + [ + -0.45319732782223243, + -0.6237726084203683, + 0.0 + ], + [ + -0.45319732782223243, + 0.6237726084203683, + 0.0 + ], + [ + 0.45319732782223243, + -0.6237726084203683, + 0.0 + ], + [ + 0.45319732782223243, + 0.6237726084203683, + 0.0 + ], + [ + -0.7332886800270005, + -0.23825993516540184, + 0.0 + ], + [ + -0.7332886800270005, + 0.23825993516540184, + 0.0 + ], + [ + 0.7332886800270005, + -0.23825993516540184, + 0.0 + ], + [ + 0.7332886800270005, + 0.23825993516540184, + 0.0 + ], + [ + 0.6558733342685862, + 0.0, + 0.4053520128927074 + ] + ], + "short_name": "J32" + }, + "Pentagonal Rotunda": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.8491786784900209, + 0.0 + ], + [ + 0.0, + 0.8491786784900209, + 0.0 + ], + [ + -0.49913470377764585, + -0.6869999821592865, + 0.0 + ], + [ + -0.49913470377764585, + 0.6869999821592865, + 0.0 + ], + [ + 0.49913470377764585, + -0.6869999821592865, + 0.0 + ], + [ + 0.49913470377764585, + 0.6869999821592865, + 0.0 + ], + [ + -0.8076169156768416, + -0.26241064291427607, + 0.0 + ], + [ + -0.8076169156768416, + 0.26241064291427607, + 0.0 + ], + [ + 0.8076169156768416, + -0.26241064291427607, + 0.0 + ], + [ + 0.8076169156768416, + 0.26241064291427607, + 0.0 + ], + [ + 0.7223545292928533, + 0.0, + 0.44643965103041483 + ], + [ + 0.22321982551520742, + -0.6869999821592865, + 0.44643965103041483 + ], + [ + 0.22321982551520742, + 0.6869999821592865, + 0.44643965103041483 + ], + [ + -0.584397090161634, + -0.42458933924501047, + 0.44643965103041483 + ], + [ + -0.584397090161634, + 0.42458933924501047, + 0.44643965103041483 + ], + [ + -0.44643965103041483, + 0.0, + 0.7223545292928533 + ], + [ + -0.1379574391312192, + -0.42458933924501047, + 0.7223545292928533 + ], + [ + -0.1379574391312192, + 0.42458933924501047, + 0.7223545292928533 + ], + [ + 0.36117726464642663, + -0.26241064291427607, + 0.7223545292928533 + ], + [ + 0.36117726464642663, + 0.26241064291427607, + 0.7223545292928533 + ] + ], + "short_name": "J06" + }, + "Square Pyramid": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + 0.0, + 1.1447142425533319 + ], + [ + 0.0, + -1.1447142425533319, + 0.0 + ], + [ + 0.0, + 1.1447142425533319, + 0.0 + ], + [ + -1.1447142425533319, + 0.0, + 0.0 + ], + [ + 1.1447142425533319, + 0.0, + 0.0 + ] + ], + "short_name": "J01" + }, + "Pentagonal Pyramid": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + 0.0, + 0.7840309614224682 + ], + [ + 1.268588743813811, + 0.0, + 0.0 + ], + [ + 0.3920154807112341, + -1.2064995913028083, + 0.0 + ], + [ + 0.3920154807112341, + 1.2064995913028083, + 0.0 + ], + [ + -1.0263098526181398, + -0.7456577548379926, + 0.0 + ], + [ + -1.0263098526181398, + 0.7456577548379926, + 0.0 + ] + ], + "short_name": "J02" + }, + "Snub Disphenoid": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.5258829786655914, + 0.0, + 0.0 + ], + [ + 0.0, + -0.5258829786655914, + 1.6490237180139626 + ], + [ + 0.0, + 0.5258829786655914, + 1.6490237180139626 + ], + [ + 0.0, + -0.6779517952082281, + 0.6083092019068308 + ], + [ + 0.0, + 0.677951795208228, + 0.6083092019068308 + ], + [ + 0.5258829786655914, + 0.0, + 0.0 + ], + [ + -0.6779517952082281, + 0.0, + 1.0407145161071318 + ], + [ + 0.677951795208228, + 0.0, + 1.0407145161071318 + ] + ], + "short_name": "J84" + }, + "Snub Square Antiprism": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.791500308223704, + 0.0, + 0.12109078717442423 + ], + [ + -0.5596752352562235, + -0.5596752352562235, + -0.12109078717442423 + ], + [ + -0.5596752352562235, + 0.5596752352562235, + -0.12109078717442423 + ], + [ + -0.4613193841416018, + 0.0, + -0.4415918105144173 + ], + [ + -0.3262020648193285, + -0.3262020648193285, + 0.4415918105144173 + ], + [ + -0.3262020648193285, + 0.3262020648193285, + 0.4415918105144173 + ], + [ + 0.0, + -0.791500308223704, + 0.12109078717442423 + ], + [ + 0.0, + -0.4613193841416018, + -0.4415918105144173 + ], + [ + 0.0, + 0.4613193841416018, + -0.4415918105144173 + ], + [ + 0.0, + 0.791500308223704, + 0.12109078717442423 + ], + [ + 0.3262020648193285, + -0.3262020648193285, + 0.4415918105144173 + ], + [ + 0.3262020648193285, + 0.3262020648193285, + 0.4415918105144173 + ], + [ + 0.4613193841416018, + 0.0, + -0.4415918105144173 + ], + [ + 0.5596752352562235, + -0.5596752352562235, + -0.12109078717442423 + ], + [ + 0.5596752352562235, + 0.5596752352562235, + -0.12109078717442423 + ], + [ + 0.791500308223704, + 0.0, + 0.12109078717442423 + ] + ], + "short_name": "J85" + }, + "Sphenocorona": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.4353102197984992, + 0.0 + ], + [ + 0.0, + 0.4353102197984992, + 0.0 + ], + [ + -0.742401505837152, + 0.4353102197984992, + 0.4547746188770872 + ], + [ + -0.4353102197984992, + 0.0, + 1.1433818395930622 + ], + [ + -0.742401505837152, + -0.4353102197984992, + 0.4547746188770872 + ], + [ + 0.742401505837152, + 0.4353102197984992, + 0.4547746188770872 + ], + [ + 0.4353102197984992, + 0.0, + 1.1433818395930622 + ], + [ + 0.742401505837152, + -0.4353102197984992, + 0.4547746188770872 + ], + [ + 0.0, + 0.6872918273535032, + 0.8333577978863982 + ], + [ + 0.0, + -0.6872918273535032, + 0.8333577978863982 + ] + ], + "short_name": "J86" + }, + "Sphenomegacorona": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.4003430658740593, + 0.0, + -0.6892621967715241 + ], + [ + 0.0, + -0.4003430658740593, + 0.6437492578983135 + ], + [ + 0.0, + 0.4003430658740593, + 0.6437492578983135 + ], + [ + 0.0, + -1.0273622483157727, + 0.14580827100941418 + ], + [ + 0.0, + 1.0273622483157727, + 0.14580827100941418 + ], + [ + 0.0, + -0.6843809323565526, + -0.5776985350930904 + ], + [ + 0.0, + 0.6843809323565526, + -0.5776985350930904 + ], + [ + 0.4003430658740593, + 0.0, + -0.6892621967715241 + ], + [ + -0.4761146653161781, + -0.4003430658740593, + 0.0 + ], + [ + -0.4761146653161781, + 0.4003430658740593, + 0.0 + ], + [ + 0.4761146653161781, + -0.4003430658740593, + 0.0 + ], + [ + 0.4761146653161781, + 0.4003430658740593, + 0.0 + ] + ], + "short_name": "J88" + }, + "Square Cupola": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.5666848865408775, + 0.5666848865408775 + ], + [ + 0.0, + 0.5666848865408775, + 0.5666848865408775 + ], + [ + -0.5666848865408775, + 0.0, + 0.5666848865408775 + ], + [ + 0.5666848865408775, + 0.0, + 0.5666848865408775 + ], + [ + 0.4007067260689838, + 0.9673916126098612, + 0.0 + ], + [ + -0.4007067260689838, + 0.9673916126098612, + 0.0 + ], + [ + -0.9673916126098612, + 0.4007067260689838, + 0.0 + ], + [ + -0.9673916126098612, + -0.4007067260689838, + 0.0 + ], + [ + -0.4007067260689838, + -0.9673916126098612, + 0.0 + ], + [ + 0.4007067260689838, + -0.9673916126098612, + 0.0 + ], + [ + 0.9673916126098612, + -0.4007067260689838, + 0.0 + ], + [ + 0.9673916126098612, + 0.4007067260689838, + 0.0 + ] + ], + "short_name": "J04" + }, + "Square Gyrobicupola": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.318041139246319, + -0.318041139246319, + -0.44977809251473433 + ], + [ + -0.318041139246319, + 0.318041139246319, + -0.44977809251473433 + ], + [ + 0.0, + -0.44977809251473433, + 0.44977809251473433 + ], + [ + 0.0, + 0.44977809251473433, + 0.44977809251473433 + ], + [ + 0.318041139246319, + -0.318041139246319, + -0.44977809251473433 + ], + [ + 0.318041139246319, + 0.318041139246319, + -0.44977809251473433 + ], + [ + -0.44977809251473433, + 0.0, + 0.44977809251473433 + ], + [ + 0.44977809251473433, + 0.0, + 0.44977809251473433 + ], + [ + 0.318041139246319, + 0.7678192317610533, + 0.0 + ], + [ + -0.318041139246319, + 0.7678192317610533, + 0.0 + ], + [ + -0.7678192317610533, + 0.318041139246319, + 0.0 + ], + [ + -0.7678192317610533, + -0.318041139246319, + 0.0 + ], + [ + -0.318041139246319, + -0.7678192317610533, + 0.0 + ], + [ + 0.318041139246319, + -0.7678192317610533, + 0.0 + ], + [ + 0.7678192317610533, + -0.318041139246319, + 0.0 + ], + [ + 0.7678192317610533, + 0.318041139246319, + 0.0 + ] + ], + "short_name": "J29" + }, + "Square Orthobicupola": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.44977809251473433, + -0.44977809251473433 + ], + [ + 0.0, + -0.44977809251473433, + 0.44977809251473433 + ], + [ + 0.0, + 0.44977809251473433, + -0.44977809251473433 + ], + [ + 0.0, + 0.44977809251473433, + 0.44977809251473433 + ], + [ + -0.44977809251473433, + 0.0, + -0.44977809251473433 + ], + [ + -0.44977809251473433, + 0.0, + 0.44977809251473433 + ], + [ + 0.44977809251473433, + 0.0, + -0.44977809251473433 + ], + [ + 0.44977809251473433, + 0.0, + 0.44977809251473433 + ], + [ + 0.318041139246319, + 0.7678192317610533, + 0.0 + ], + [ + -0.318041139246319, + 0.7678192317610533, + 0.0 + ], + [ + -0.7678192317610533, + 0.318041139246319, + 0.0 + ], + [ + -0.7678192317610533, + -0.318041139246319, + 0.0 + ], + [ + -0.318041139246319, + -0.7678192317610533, + 0.0 + ], + [ + 0.318041139246319, + -0.7678192317610533, + 0.0 + ], + [ + 0.7678192317610533, + -0.318041139246319, + 0.0 + ], + [ + 0.7678192317610533, + 0.318041139246319, + 0.0 + ] + ], + "short_name": "J28" + }, + "Triangular Cupola": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.9467211571056353, + 0.0 + ], + [ + 0.0, + 0.9467211571056353, + 0.0 + ], + [ + -0.2732948574512263, + -0.47336057855281766, + 0.7729945878686918 + ], + [ + -0.2732948574512263, + 0.47336057855281766, + 0.7729945878686918 + ], + [ + 0.5465897149024526, + 0.0, + 0.7729945878686918 + ], + [ + -0.8198845723536787, + -0.47336057855281766, + 0.0 + ], + [ + -0.8198845723536787, + 0.47336057855281766, + 0.0 + ], + [ + 0.8198845723536787, + -0.47336057855281766, + 0.0 + ], + [ + 0.8198845723536787, + 0.47336057855281766, + 0.0 + ] + ], + "short_name": "J03" + }, + "Triangular Hebesphenorotunda": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.7600471158859848, + -0.1035897934793219, + -0.1596090550798997 + ], + [ + -0.7600471158859848, + 0.4388134069535721, + 0.047570531878744195 + ], + [ + -0.5806243304342321, + 0.0, + 0.3827941453529943 + ], + [ + -0.4697349506688688, + -0.6064252136906972, + -0.1596090550798997 + ], + [ + -0.29031216521711606, + -0.5028354202113752, + 0.3827941453529943 + ], + [ + -0.29031216521711606, + -0.16761180673712509, + -0.4948326685541498 + ], + [ + -0.29031216521711606, + 0.5028354202113752, + 0.3827941453529943 + ], + [ + -0.29031216521711606, + 0.7100150071700191, + -0.1596090550798997 + ], + [ + 0.0, + -0.8776268139071443, + 0.047570531878744195 + ], + [ + 0.0, + 0.33522361347425017, + -0.4948326685541498 + ], + [ + 0.29031216521711606, + -0.5028354202113752, + 0.3827941453529943 + ], + [ + 0.29031216521711606, + -0.16761180673712509, + -0.4948326685541498 + ], + [ + 0.29031216521711606, + 0.5028354202113752, + 0.3827941453529943 + ], + [ + 0.29031216521711606, + 0.7100150071700191, + -0.1596090550798997 + ], + [ + 0.4697349506688688, + -0.6064252136906972, + -0.1596090550798997 + ], + [ + 0.5806243304342321, + 0.0, + 0.3827941453529943 + ], + [ + 0.7600471158859848, + -0.1035897934793219, + -0.1596090550798997 + ], + [ + 0.7600471158859848, + 0.4388134069535721, + 0.047570531878744195 + ] + ], + "short_name": "J92" + }, + "Triangular Orthobicupola": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.7514130803550182, + 0.0 + ], + [ + 0.0, + 0.7514130803550182, + 0.0 + ], + [ + -0.21691427210778785, + -0.3757065401775091, + -0.613526210974243 + ], + [ + -0.21691427210778785, + -0.3757065401775091, + 0.613526210974243 + ], + [ + -0.21691427210778785, + 0.3757065401775091, + -0.613526210974243 + ], + [ + -0.21691427210778785, + 0.3757065401775091, + 0.613526210974243 + ], + [ + 0.4338285442155757, + 0.0, + -0.613526210974243 + ], + [ + 0.4338285442155757, + 0.0, + 0.613526210974243 + ], + [ + -0.6507428163233634, + -0.3757065401775091, + 0.0 + ], + [ + -0.6507428163233634, + 0.3757065401775091, + 0.0 + ], + [ + 0.6507428163233634, + -0.3757065401775091, + 0.0 + ], + [ + 0.6507428163233634, + 0.3757065401775091, + 0.0 + ] + ], + "short_name": "J27" + }, + "Triaugmented Dodecahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + 0.0, + 0.6848015698857872 + ], + [ + 0.0, + 0.0, + -0.6848015698857873 + ], + [ + 0.0871903080490281, + -0.6397226979615769, + 0.2282671899619291 + ], + [ + 0.0871903080490281, + 0.6397226979615769, + 0.2282671899619291 + ], + [ + 0.2282671899619291, + -0.3953703707150376, + -0.5104209537877311 + ], + [ + 0.2282671899619291, + 0.3953703707150376, + -0.5104209537877311 + ], + [ + 0.5104209537877311, + -0.3953703707150376, + 0.2282671899619291 + ], + [ + 0.5104209537877311, + 0.3953703707150376, + 0.2282671899619291 + ], + [ + -0.5976112618367592, + -0.2443523272465393, + 0.2282671899619291 + ], + [ + -0.5976112618367592, + 0.2443523272465393, + 0.2282671899619291 + ], + [ + 0.5976112618367592, + -0.2443523272465393, + -0.22826718996192907 + ], + [ + 0.5976112618367592, + 0.2443523272465393, + -0.22826718996192907 + ], + [ + -0.45653437992385815, + 0.0, + -0.5104209537877311 + ], + [ + -0.22826718996192907, + -0.3953703707150376, + 0.5104209537877311 + ], + [ + -0.22826718996192907, + 0.3953703707150376, + 0.5104209537877311 + ], + [ + 0.4565343799238582, + 0.0, + 0.5104209537877311 + ], + [ + -0.5104209537877311, + -0.3953703707150376, + -0.22826718996192907 + ], + [ + -0.5104209537877311, + 0.3953703707150376, + -0.22826718996192907 + ], + [ + -0.4863221453408944, + 0.0, + 0.636603952992114 + ], + [ + -0.0871903080490281, + -0.6397226979615769, + -0.22826718996192907 + ], + [ + -0.0871903080490281, + 0.6397226979615769, + -0.22826718996192907 + ], + [ + 0.3934428803216667, + 0.6814630585933681, + -0.1502818076512195 + ], + [ + 0.3934428803216667, + -0.6814630585933681, + -0.1502818076512195 + ] + ], + "short_name": "J61" + }, + "Triaugmented Hexagonal Prism": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.6713281065651684, + 0.0, + -0.3356640532825842 + ], + [ + -0.6713281065651684, + 0.0, + 0.3356640532825842 + ], + [ + -0.3356640532825842, + -0.5813871945599426, + -0.3356640532825842 + ], + [ + -0.3356640532825842, + -0.5813871945599426, + 0.3356640532825842 + ], + [ + -0.3356640532825842, + 0.5813871945599426, + -0.3356640532825842 + ], + [ + -0.3356640532825842, + 0.5813871945599426, + 0.3356640532825842 + ], + [ + 0.0, + -1.0560878511132985, + 0.0 + ], + [ + 0.3356640532825842, + -0.5813871945599426, + -0.3356640532825842 + ], + [ + 0.3356640532825842, + -0.5813871945599426, + 0.3356640532825842 + ], + [ + 0.3356640532825842, + 0.5813871945599426, + -0.3356640532825842 + ], + [ + 0.3356640532825842, + 0.5813871945599426, + 0.3356640532825842 + ], + [ + 0.6713281065651684, + 0.0, + -0.3356640532825842 + ], + [ + 0.6713281065651684, + 0.0, + 0.3356640532825842 + ], + [ + -0.9145989076922343, + 0.5280439255566491, + 0.0 + ], + [ + 0.9145989076922343, + 0.5280439255566491, + 0.0 + ] + ], + "short_name": "J57" + }, + "Triaugmented Triangular Prism": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.2763286537812891, + -0.47861526793630244, + -0.47861526793630244 + ], + [ + -0.2763286537812891, + -0.47861526793630244, + 0.47861526793630244 + ], + [ + -0.2763286537812891, + 0.47861526793630244, + -0.47861526793630244 + ], + [ + -0.2763286537812891, + 0.47861526793630244, + 0.47861526793630244 + ], + [ + 0.5526573075625782, + 0.0, + -0.47861526793630244 + ], + [ + 0.5526573075625782, + 0.0, + 0.47861526793630244 + ], + [ + -0.9531928568556407, + 0.0, + 0.0 + ], + [ + 0.47659642842782035, + -0.8254892287428488, + 0.0 + ], + [ + 0.47659642842782035, + 0.8254892287428488, + 0.0 + ] + ], + "short_name": "J51" + }, + "Triaugmented Truncated Dodecahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.541736108434475, + -0.3584042331517614, + 0.1034623902444354 + ], + [ + -0.541736108434475, + -0.3584042331517614, + -0.1034623902444354 + ], + [ + 0.541736108434475, + 0.3584042331517614, + 0.1034623902444354 + ], + [ + -0.541736108434475, + 0.3584042331517614, + -0.1034623902444354 + ], + [ + 0.039519116516068785, + -0.6483593486274573, + 0.1034623902444354 + ], + [ + 0.039519116516068785, + 0.6483593486274573, + 0.1034623902444354 + ], + [ + 0.3987546016739707, + -0.46915723205157656, + 0.2313489377011687 + ], + [ + 0.3987546016739707, + 0.46915723205157656, + 0.2313489377011687 + ], + [ + -0.12788654745673325, + 0.0, + -0.6451984986789104 + ], + [ + 0.1429815067605042, + -0.46915723205157656, + -0.4382737181900395 + ], + [ + 0.1429815067605042, + 0.46915723205157656, + -0.4382737181900395 + ], + [ + 0.0, + -0.5799102309513917, + -0.31038717073330624 + ], + [ + 0.0, + 0.5799102309513917, + -0.31038717073330624 + ], + [ + -0.39875460167397075, + -0.46915723205157656, + -0.2313489377011687 + ], + [ + -0.39875460167397075, + 0.46915723205157656, + -0.2313489377011687 + ], + [ + 0.0, + -0.5799102309513917, + 0.31038717073330624 + ], + [ + 0.0, + 0.5799102309513917, + 0.31038717073330624 + ], + [ + 0.12788654745673325, + 0.0, + 0.6451984986789104 + ], + [ + -0.5022169919184061, + -0.28995511547569586, + 0.31038717073330624 + ], + [ + -0.5022169919184061, + 0.28995511547569586, + 0.31038717073330624 + ], + [ + -0.1429815067605042, + -0.46915723205157656, + 0.4382737181900395 + ], + [ + -0.1429815067605042, + 0.46915723205157656, + 0.4382737181900395 + ], + [ + 0.3348113279456041, + 0.0, + 0.5661602656467727 + ], + [ + -0.33481132794560414, + -0.3584042331517614, + 0.4382737181900395 + ], + [ + -0.33481132794560414, + 0.3584042331517614, + 0.4382737181900395 + ], + [ + 0.16740566397280207, + -0.28995511547569586, + -0.5661602656467727 + ], + [ + 0.16740566397280207, + 0.28995511547569586, + -0.5661602656467727 + ], + [ + -0.16740566397280207, + -0.28995511547569586, + 0.5661602656467727 + ], + [ + -0.16740566397280207, + 0.28995511547569586, + 0.5661602656467727 + ], + [ + -0.06394327372836663, + -0.11075299889981519, + 0.6451984986789104 + ], + [ + -0.06394327372836663, + 0.11075299889981519, + 0.6451984986789104 + ], + [ + 0.06394327372836663, + -0.11075299889981519, + -0.6451984986789103 + ], + [ + 0.06394327372836663, + 0.11075299889981519, + -0.6451984986789103 + ], + [ + 0.5022169919184061, + -0.28995511547569586, + 0.31038717073330624 + ], + [ + -0.5812552249505436, + -0.28995511547569586, + 0.1034623902444354 + ], + [ + 0.5022169919184061, + 0.28995511547569586, + 0.31038717073330624 + ], + [ + -0.5812552249505436, + 0.28995511547569586, + 0.1034623902444354 + ], + [ + 0.2069247804888708, + -0.5799102309513917, + 0.23134893770116866 + ], + [ + 0.2069247804888708, + 0.5799102309513917, + 0.23134893770116866 + ], + [ + 0.5812552249505436, + -0.28995511547569586, + -0.1034623902444354 + ], + [ + -0.5022169919184061, + -0.28995511547569586, + -0.31038717073330624 + ], + [ + 0.5812552249505436, + 0.28995511547569586, + -0.1034623902444354 + ], + [ + -0.5022169919184061, + 0.28995511547569586, + -0.31038717073330624 + ], + [ + 0.6056793821628416, + -0.11075299889981519, + -0.23134893770116866 + ], + [ + -0.47779283470610834, + -0.11075299889981519, + -0.4382737181900395 + ], + [ + 0.6056793821628416, + 0.11075299889981519, + -0.23134893770116866 + ], + [ + -0.47779283470610834, + 0.11075299889981519, + -0.4382737181900395 + ], + [ + 0.4777928347061082, + -0.11075299889981519, + 0.4382737181900395 + ], + [ + -0.6056793821628416, + -0.11075299889981519, + 0.23134893770116866 + ], + [ + 0.4777928347061082, + 0.11075299889981519, + 0.4382737181900395 + ], + [ + -0.6056793821628416, + 0.11075299889981519, + 0.23134893770116866 + ], + [ + -0.3348113279456041, + 0.0, + -0.5661602656467728 + ], + [ + 0.3348113279456041, + -0.3584042331517614, + -0.4382737181900395 + ], + [ + 0.3348113279456041, + 0.3584042331517614, + -0.4382737181900395 + ], + [ + -0.2069247804888708, + -0.5799102309513917, + -0.23134893770116866 + ], + [ + -0.2069247804888708, + 0.5799102309513917, + -0.23134893770116866 + ], + [ + 0.5022169919184061, + -0.28995511547569586, + -0.31038717073330624 + ], + [ + 0.5022169919184061, + 0.28995511547569586, + -0.31038717073330624 + ], + [ + -0.03951911651606878, + -0.6483593486274573, + -0.1034623902444354 + ], + [ + -0.03951911651606878, + 0.6483593486274573, + -0.1034623902444354 + ], + [ + -0.691468286219144, + 0.0, + 0.059771129588563586 + ], + [ + -0.6670441290068462, + 0.1792021165758807, + -0.06811541786816962 + ], + [ + -0.6275250124907773, + 0.11075299889981519, + -0.2750401983570405 + ], + [ + -0.6275250124907773, + -0.11075299889981519, + -0.2750401983570405 + ], + [ + -0.6670441290068462, + -0.1792021165758807, + -0.06811541786816962 + ], + [ + 0.345734143109572, + -0.5988291017770679, + 0.059771129588563586 + ], + [ + 0.17832847913676997, + -0.6672782194531335, + -0.06811541786816962 + ], + [ + 0.2178475956528388, + -0.5988291017770679, + -0.2750401983570405 + ], + [ + 0.4096774168379386, + -0.4880761028772528, + -0.2750401983570405 + ], + [ + 0.4887156498700762, + -0.4880761028772528, + -0.06811541786816962 + ], + [ + 0.345734143109572, + 0.5988291017770679, + 0.059771129588563586 + ], + [ + 0.4887156498700762, + 0.4880761028772528, + -0.06811541786816962 + ], + [ + 0.4096774168379386, + 0.4880761028772528, + -0.2750401983570405 + ], + [ + 0.2178475956528388, + 0.5988291017770679, + -0.2750401983570405 + ], + [ + 0.17832847913676997, + 0.6672782194531335, + -0.06811541786816962 + ] + ], + "short_name": "J71" + }, + "Tridiminished Icosahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.5321343166736058, + 0.0, + -0.6965728638158498 + ], + [ + -0.2660671583368029, + -0.46084183646481575, + 0.6965728638158498 + ], + [ + -0.2660671583368029, + 0.46084183646481575, + 0.6965728638158498 + ], + [ + 0.2660671583368029, + -0.46084183646481575, + -0.6965728638158498 + ], + [ + 0.2660671583368029, + 0.46084183646481575, + -0.6965728638158498 + ], + [ + 0.5321343166736058, + 0.0, + 0.6965728638158498 + ], + [ + 0.43050570547904704, + -0.7456577548379926, + 0.16443854714224412 + ], + [ + 0.43050570547904704, + 0.7456577548379926, + 0.16443854714224412 + ], + [ + -0.861011410958094, + 0.0, + 0.16443854714224412 + ] + ], + "short_name": "J63" + }, + "Tridiminished Rhombicosidodecahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.15337834766884678, + 0.0885530303144687, + -0.6616802817369094 + ], + [ + -0.15337834766884678, + -0.37511665602568905, + 0.5522227166546264 + ], + [ + -0.15337834766884678, + 0.375116656025689, + -0.5522227166546264 + ], + [ + -0.15337834766884678, + -0.0885530303144687, + 0.6616802817369093 + ], + [ + -0.15337834766884678, + -0.5522227166546264, + -0.37511665602568905 + ], + [ + -0.15337834766884678, + 0.6616802817369093, + 0.0885530303144687 + ], + [ + -0.15337834766884678, + 0.5522227166546264, + 0.375116656025689 + ], + [ + 0.0, + -0.1771060606289374, + -0.6616802817369093 + ], + [ + 0.0, + 0.5731272514224406, + -0.37511665602568905 + ], + [ + 0.0, + 0.1771060606289374, + 0.6616802817369093 + ], + [ + 0.15337834766884678, + 0.0885530303144687, + -0.6616802817369094 + ], + [ + 0.15337834766884678, + -0.37511665602568905, + 0.5522227166546264 + ], + [ + 0.15337834766884678, + 0.375116656025689, + -0.5522227166546264 + ], + [ + 0.15337834766884678, + -0.0885530303144687, + 0.6616802817369093 + ], + [ + 0.15337834766884678, + -0.5522227166546264, + -0.37511665602568905 + ], + [ + 0.15337834766884678, + 0.6616802817369093, + 0.0885530303144687 + ], + [ + 0.15337834766884678, + 0.5522227166546264, + 0.375116656025689 + ], + [ + -0.5549280750041858, + 0.14328181285561015, + -0.375116656025689 + ], + [ + -0.5549280750041858, + -0.14328181285561015, + 0.375116656025689 + ], + [ + -0.2481713796664923, + -0.32038787348454756, + -0.5522227166546264 + ], + [ + -0.2481713796664923, + 0.6069514991957679, + -0.1980105953967516 + ], + [ + -0.2481713796664923, + 0.32038787348454756, + 0.5522227166546264 + ], + [ + -0.4963427593329846, + -0.2865636257112203, + -0.375116656025689 + ], + [ + -0.4963427593329846, + -0.4636696863401578, + 0.0885530303144687 + ], + [ + -0.6497211070018314, + -0.0885530303144687, + -0.1980105953967516 + ], + [ + -0.6497211070018314, + -0.1980105953967516, + 0.0885530303144687 + ], + [ + -0.40154972733533917, + -0.5183984688812991, + -0.1980105953967516 + ], + [ + -0.40154972733533917, + -0.05472878254114145, + -0.5522227166546264 + ], + [ + -0.40154972733533917, + -0.4089409037990163, + 0.375116656025689 + ], + [ + -0.40154972733533917, + 0.4089409037990163, + -0.37511665602568905 + ], + [ + -0.40154972733533917, + 0.05472878254114145, + 0.5522227166546264 + ], + [ + 0.2481713796664923, + -0.32038787348454756, + -0.5522227166546264 + ], + [ + 0.2481713796664923, + 0.6069514991957679, + -0.1980105953967516 + ], + [ + 0.2481713796664923, + 0.32038787348454756, + 0.5522227166546264 + ], + [ + 0.4963427593329846, + -0.2865636257112203, + -0.375116656025689 + ], + [ + 0.4963427593329846, + -0.4636696863401578, + 0.0885530303144687 + ], + [ + 0.6497211070018314, + -0.0885530303144687, + -0.1980105953967516 + ], + [ + 0.6497211070018314, + -0.1980105953967516, + 0.0885530303144687 + ], + [ + 0.40154972733533906, + -0.5183984688812991, + -0.1980105953967516 + ], + [ + 0.40154972733533906, + -0.05472878254114145, + -0.5522227166546264 + ], + [ + 0.40154972733533906, + -0.4089409037990163, + 0.375116656025689 + ], + [ + 0.40154972733533906, + 0.4089409037990163, + -0.37511665602568905 + ], + [ + 0.40154972733533906, + 0.05472878254114145, + 0.5522227166546264 + ], + [ + 0.5549280750041858, + 0.14328181285561015, + -0.375116656025689 + ], + [ + 0.5549280750041858, + -0.14328181285561015, + 0.375116656025689 + ] + ], + "short_name": "J83" + }, + "Trigyrate Rhombicosidodecahedron": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.1442842451438814, + 0.0833025477736419, + -0.6224479623624998 + ], + [ + -0.1442842451438814, + -0.3528752550680709, + 0.5194803506153546 + ], + [ + -0.1442842451438814, + 0.3528752550680708, + -0.5194803506153547 + ], + [ + -0.1442842451438814, + -0.0833025477736419, + 0.6224479623624997 + ], + [ + -0.1442842451438814, + -0.5194803506153547, + -0.3528752550680709 + ], + [ + 0.0, + -0.631242446327827, + -0.1293510636431264 + ], + [ + -0.1442842451438814, + 0.6224479623624997, + 0.0833025477736419 + ], + [ + -0.1442842451438814, + 0.5194803506153546, + 0.3528752550680708 + ], + [ + 0.0, + -0.1666050955472838, + -0.6224479623624997 + ], + [ + -0.1442842451438814, + -0.5479398985541849, + 0.30682673919858633 + ], + [ + 0.0, + 0.5391454145888578, + -0.3528752550680709 + ], + [ + 0.0, + 0.1666050955472838, + 0.6224479623624997 + ], + [ + 0.1442842451438814, + 0.0833025477736419, + -0.6224479623624998 + ], + [ + 0.1442842451438814, + -0.3528752550680709, + 0.5194803506153546 + ], + [ + 0.1442842451438814, + 0.3528752550680708, + -0.5194803506153547 + ], + [ + 0.1442842451438814, + -0.0833025477736419, + 0.6224479623624997 + ], + [ + 0.1442842451438814, + -0.5194803506153547, + -0.3528752550680709 + ], + [ + 0.2334568126839221, + -0.5994237044277576, + 0.0372540319041574 + ], + [ + 0.1442842451438814, + 0.6224479623624997, + 0.0833025477736419 + ], + [ + 0.1442842451438814, + 0.5194803506153546, + 0.3528752550680708 + ], + [ + -0.5220253029716849, + 0.13478635364721445, + -0.3528752550680708 + ], + [ + -0.5220253029716849, + -0.13478635364721445, + 0.3528752550680708 + ], + [ + -0.2334568126839221, + -0.30139144919449823, + -0.5194803506153546 + ], + [ + -0.2334568126839221, + -0.5994237044277576, + 0.0372540319041574 + ], + [ + -0.2334568126839221, + 0.5709641564889272, + -0.18627015952078702 + ], + [ + -0.2334568126839221, + 0.30139144919449823, + 0.5194803506153546 + ], + [ + -0.4669136253678442, + -0.2695727072944289, + -0.3528752550680708 + ], + [ + -0.4669136253678442, + -0.4361778028417128, + 0.0833025477736419 + ], + [ + -0.546671994466933, + 0.3156212231639134, + -0.1293510636431264 + ], + [ + -0.4023877493230516, + 0.39892377093755527, + 0.30682673919858633 + ], + [ + -0.6111978705117256, + -0.0833025477736419, + -0.18627015952078702 + ], + [ + -0.6111978705117256, + -0.18627015952078702, + 0.0833025477736419 + ], + [ + -0.6358445620069737, + 0.09753232174305705, + 0.0372540319041574 + ], + [ + -0.546671994466933, + 0.1490161276166296, + 0.30682673919858633 + ], + [ + -0.3777410578278036, + -0.4876616087152853, + -0.18627015952078702 + ], + [ + -0.3777410578278036, + -0.05148380587357257, + -0.5194803506153547 + ], + [ + -0.3777410578278036, + -0.38469399696814016, + 0.3528752550680708 + ], + [ + -0.3777410578278036, + 0.38469399696814016, + -0.3528752550680709 + ], + [ + -0.3777410578278036, + 0.05148380587357257, + 0.5194803506153546 + ], + [ + -0.4023877493230516, + 0.5018913826847005, + 0.0372540319041574 + ], + [ + 0.2334568126839221, + -0.30139144919449823, + -0.5194803506153546 + ], + [ + 0.1442842451438814, + -0.5479398985541849, + 0.30682673919858633 + ], + [ + 0.2334568126839221, + 0.5709641564889272, + -0.18627015952078702 + ], + [ + 0.2334568126839221, + 0.30139144919449823, + 0.5194803506153546 + ], + [ + 0.4669136253678442, + -0.2695727072944289, + -0.3528752550680708 + ], + [ + 0.4669136253678442, + -0.4361778028417128, + 0.0833025477736419 + ], + [ + 0.4023877493230516, + 0.5018913826847005, + 0.0372540319041574 + ], + [ + 0.546671994466933, + 0.1490161276166296, + 0.30682673919858633 + ], + [ + 0.6111978705117256, + -0.0833025477736419, + -0.18627015952078702 + ], + [ + 0.6111978705117256, + -0.18627015952078702, + 0.0833025477736419 + ], + [ + 0.546671994466933, + 0.3156212231639134, + -0.1293510636431264 + ], + [ + 0.6358445620069737, + 0.09753232174305705, + 0.0372540319041574 + ], + [ + 0.3777410578278035, + -0.4876616087152853, + -0.18627015952078702 + ], + [ + 0.3777410578278035, + -0.05148380587357257, + -0.5194803506153547 + ], + [ + 0.3777410578278035, + -0.38469399696814016, + 0.3528752550680708 + ], + [ + 0.3777410578278035, + 0.38469399696814016, + -0.3528752550680709 + ], + [ + 0.3777410578278035, + 0.05148380587357257, + 0.5194803506153546 + ], + [ + 0.4023877493230516, + 0.39892377093755527, + 0.30682673919858633 + ], + [ + 0.5220253029716849, + 0.13478635364721445, + -0.3528752550680708 + ], + [ + 0.5220253029716849, + -0.13478635364721445, + 0.3528752550680708 + ] + ], + "short_name": "J75" + } +} diff --git a/coxeter/families/data/platonic.json b/coxeter/families/data/platonic.json index a0b3c14f..3b71287a 100644 --- a/coxeter/families/data/platonic.json +++ b/coxeter/families/data/platonic.json @@ -42,112 +42,116 @@ 0.5, 0.5 ] - ] + ], + "symmetry_group": "[4,3]", + "short_code": "P03" }, "Dodecahedron": { "type": "ConvexPolyhedron", "vertices": [ [ - -0.69813, + -0.6981312901399714, 0.0, - 0.13333 + 0.13333121211182739 ], [ - 0.69813, + 0.6981312901399714, 0.0, - -0.13333 + -0.13333121211182739 ], [ - -0.21573, - -0.66396, - 0.13333 + -0.21573443295815836, + -0.6639623127171623, + 0.13333121211182739 ], [ - -0.21573, - 0.66396, - 0.13333 + -0.21573443295815836, + 0.6639623127171623, + 0.13333121211182739 ], [ - 0.5648, - -0.41035, - 0.13333 + 0.564800078028144, + -0.41035127650819286, + 0.13333121211182739 ], [ - 0.5648, - 0.41035, - 0.13333 + 0.564800078028144, + 0.41035127650819286, + 0.13333121211182739 ], [ - -0.13333, - -0.41035, - 0.5648 + -0.13333121211182739, + -0.41035127650819286, + 0.564800078028144 ], [ - -0.13333, - 0.41035, - 0.5648 + -0.13333121211182739, + 0.41035127650819286, + 0.564800078028144 ], [ - -0.34907, - -0.25361, - -0.5648 + -0.3490656450699857, + -0.25361103620896946, + -0.564800078028144 ], [ - -0.34907, - 0.25361, - -0.5648 + -0.3490656450699857, + 0.25361103620896946, + -0.564800078028144 ], [ - 0.34907, - -0.25361, - 0.5648 + 0.3490656450699857, + -0.25361103620896946, + 0.564800078028144 ], [ - 0.34907, - 0.25361, - 0.5648 + 0.3490656450699857, + 0.25361103620896946, + 0.564800078028144 ], [ - 0.43147, + 0.4314688659163167, 0.0, - -0.5648 + -0.564800078028144 ], [ - -0.5648, - -0.41035, - -0.13333 + -0.564800078028144, + -0.41035127650819286, + -0.13333121211182739 ], [ - -0.5648, - 0.41035, - -0.13333 + -0.564800078028144, + 0.41035127650819286, + -0.13333121211182739 ], [ - -0.43147, + -0.4314688659163167, 0.0, - 0.5648 + 0.564800078028144 ], [ - 0.13333, - -0.41035, - -0.5648 + 0.13333121211182739, + -0.41035127650819286, + -0.564800078028144 ], [ - 0.13333, - 0.41035, - -0.5648 + 0.13333121211182739, + 0.41035127650819286, + -0.564800078028144 ], [ - 0.21573, - -0.66396, - -0.13333 + 0.21573443295815833, + -0.6639623127171623, + -0.13333121211182739 ], [ - 0.21573, - 0.66396, - -0.13333 + 0.21573443295815833, + 0.6639623127171623, + -0.13333121211182739 ] - ] + ], + "symmetry_group": "[5,3]", + "short_code": "P05" }, "Icosahedron": { "type": "ConvexPolyhedron", @@ -155,99 +159,103 @@ [ 0.0, 0.0, - -0.73329 + -0.7332886800270006 ], [ 0.0, 0.0, - 0.73329 + 0.7332886800270006 ], [ - -0.65587, + -0.6558733342685863, 0.0, - -0.32794 + -0.3279366671342931 ], [ - 0.65587, + 0.6558733342685863, 0.0, - 0.32794 + 0.3279366671342931 ], [ - 0.53061, - -0.38551, - -0.32794 + 0.5306126735806469, + -0.3855126732549665, + -0.3279366671342931 ], [ - 0.53061, - 0.38551, - -0.32794 + 0.5306126735806469, + 0.3855126732549665, + -0.3279366671342931 ], [ - -0.53061, - -0.38551, - 0.32794 + -0.5306126735806469, + -0.3855126732549665, + 0.3279366671342931 ], [ - -0.53061, - 0.38551, - 0.32794 + -0.5306126735806469, + 0.3855126732549665, + 0.3279366671342931 ], [ - -0.20268, - -0.62377, - -0.32794 + -0.20267600644635372, + -0.6237726084203684, + -0.3279366671342931 ], [ - -0.20268, - 0.62377, - -0.32794 + -0.20267600644635372, + 0.6237726084203684, + -0.3279366671342931 ], [ - 0.20268, - -0.62377, - 0.32794 + 0.20267600644635372, + -0.6237726084203684, + 0.3279366671342931 ], [ - 0.20268, - 0.62377, - 0.32794 + 0.20267600644635372, + 0.6237726084203684, + 0.3279366671342931 ] - ] + ], + "symmetry_group": "[5,3]", + "short_code": "P04" }, "Octahedron": { "type": "ConvexPolyhedron", "vertices": [ [ - -0.90856, + -0.9085602964160698, 0.0, 0.0 ], [ 0.0, - 0.90856, + 0.9085602964160698, 0.0 ], [ 0.0, 0.0, - -0.90856 + -0.9085602964160698 ], [ 0.0, 0.0, - 0.90856 + 0.9085602964160698 ], [ 0.0, - -0.90856, + -0.9085602964160698, 0.0 ], [ - 0.90856, + 0.9085602964160698, 0.0, 0.0 ] - ] + ], + "symmetry_group": "[4,3]", + "short_code": "P02" }, "Tetrahedron": { "type": "ConvexPolyhedron", @@ -255,23 +263,25 @@ [ 0.0, 0.0, - 1.24902 + 1.249024766483406 ], [ - -0.5888, - -1.01982, - -0.41634 + -0.5887959215002404, + -1.0198244513277526, + -0.41634158882780214 ], [ - -0.5888, - 1.01982, - -0.41634 + -0.5887959215002404, + 1.0198244513277526, + -0.41634158882780214 ], [ - 1.17759, + 1.1775918430004808, 0.0, - -0.41634 + -0.41634158882780214 ] - ] + ], + "symmetry_group": "[3,3]", + "short_code": "P01" } } diff --git a/coxeter/families/data/prism_antiprism.json b/coxeter/families/data/prism_antiprism.json new file mode 100644 index 00000000..97c5540f --- /dev/null +++ b/coxeter/families/data/prism_antiprism.json @@ -0,0 +1,1138 @@ +{ + "Triangular Antiprism": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.9085602964160698, + 0.0, + 0.0 + ], + [ + 0.0, + 0.9085602964160698, + 0.0 + ], + [ + 0.0, + 0.0, + -0.9085602964160698 + ], + [ + 0.0, + 0.0, + 0.9085602964160698 + ], + [ + 0.0, + -0.9085602964160698, + 0.0 + ], + [ + 0.9085602964160698, + 0.0, + 0.0 + ] + ], + "alternative_name": "Antiprism 3" + }, + "Square Antiprism": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.5073792410466191, + -0.5073792410466191, + -0.42665338497025235 + ], + [ + -0.5073792410466191, + 0.5073792410466191, + -0.42665338497025235 + ], + [ + 0.0, + -0.7175426039546965, + 0.42665338497025235 + ], + [ + 0.0, + 0.7175426039546965, + 0.42665338497025235 + ], + [ + 0.5073792410466191, + -0.5073792410466191, + -0.42665338497025235 + ], + [ + 0.5073792410466191, + 0.5073792410466191, + -0.42665338497025235 + ], + [ + -0.7175426039546965, + 0.0, + 0.42665338497025235 + ], + [ + 0.7175426039546965, + 0.0, + 0.42665338497025235 + ] + ], + "alternative_name": "Antiprism 4" + }, + "Pentagonal Antiprism": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.7305541769773849, + 0.0, + -0.36527708848869245 + ], + [ + 0.7305541769773849, + 0.0, + 0.36527708848869245 + ], + [ + -0.5910307444863074, + -0.4294089712279723, + 0.36527708848869245 + ], + [ + -0.5910307444863074, + 0.4294089712279723, + 0.36527708848869245 + ], + [ + -0.2257536559976149, + -0.6947983105209848, + -0.36527708848869245 + ], + [ + -0.2257536559976149, + 0.6947983105209848, + -0.36527708848869245 + ], + [ + 0.2257536559976149, + -0.6947983105209848, + 0.36527708848869245 + ], + [ + 0.2257536559976149, + 0.6947983105209848, + 0.36527708848869245 + ], + [ + 0.5910307444863074, + -0.4294089712279723, + -0.36527708848869245 + ], + [ + 0.5910307444863074, + 0.4294089712279723, + -0.36527708848869245 + ] + ], + "alternative_name": "Antiprism 5" + }, + "Hexagonal Antiprism": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.7534947062027737, + 0.0, + 0.3223449136872011 + ], + [ + -0.37674735310138685, + -0.652545557188694, + 0.3223449136872011 + ], + [ + -0.37674735310138685, + 0.652545557188694, + 0.3223449136872011 + ], + [ + 0.0, + -0.7534947062027737, + -0.3223449136872011 + ], + [ + 0.0, + 0.7534947062027737, + -0.3223449136872011 + ], + [ + 0.37674735310138685, + -0.652545557188694, + 0.3223449136872011 + ], + [ + 0.37674735310138685, + 0.652545557188694, + 0.3223449136872011 + ], + [ + 0.7534947062027737, + 0.0, + 0.3223449136872011 + ], + [ + -0.652545557188694, + -0.37674735310138685, + -0.3223449136872011 + ], + [ + -0.652545557188694, + 0.37674735310138685, + -0.3223449136872011 + ], + [ + 0.652545557188694, + -0.37674735310138685, + -0.3223449136872011 + ], + [ + 0.652545557188694, + 0.37674735310138685, + -0.3223449136872011 + ] + ], + "alternative_name": "Antiprism 6" + }, + "Heptagonal Antiprism": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.7020965970779439, + -0.33811190110387385, + 0.2902600045134933 + ], + [ + -0.7020965970779439, + 0.33811190110387385, + 0.2902600045134933 + ], + [ + 0.7020965970779439, + -0.33811190110387385, + -0.2902600045134933 + ], + [ + 0.7020965970779439, + 0.33811190110387385, + -0.2902600045134933 + ], + [ + -0.7792684321185508, + 0.0, + -0.2902600045134933 + ], + [ + 0.7792684321185508, + 0.0, + 0.2902600045134933 + ], + [ + -0.17340353931769273, + -0.7597305455545419, + 0.2902600045134933 + ], + [ + -0.17340353931769273, + 0.7597305455545419, + 0.2902600045134933 + ], + [ + 0.17340353931769273, + -0.7597305455545419, + -0.2902600045134933 + ], + [ + 0.17340353931769273, + 0.7597305455545419, + -0.2902600045134933 + ], + [ + -0.48586592033636117, + -0.6092565935237838, + -0.2902600045134933 + ], + [ + -0.48586592033636117, + 0.6092565935237838, + -0.2902600045134933 + ], + [ + 0.48586592033636117, + -0.6092565935237838, + 0.2902600045134933 + ], + [ + 0.48586592033636117, + 0.6092565935237838, + 0.2902600045134933 + ] + ], + "alternative_name": "Antiprism 7" + }, + "Octagonal Antiprism": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.30824544504292245, + -0.7441703339623539, + -0.26518219080086625 + ], + [ + -0.30824544504292245, + 0.7441703339623539, + -0.26518219080086625 + ], + [ + 0.0, + -0.8054841651698379, + 0.26518219080086625 + ], + [ + 0.0, + 0.8054841651698379, + 0.26518219080086625 + ], + [ + 0.30824544504292245, + -0.7441703339623539, + -0.26518219080086625 + ], + [ + 0.30824544504292245, + 0.7441703339623539, + -0.26518219080086625 + ], + [ + -0.7441703339623539, + -0.30824544504292245, + -0.26518219080086625 + ], + [ + -0.7441703339623539, + 0.30824544504292245, + -0.26518219080086625 + ], + [ + 0.7441703339623539, + -0.30824544504292245, + -0.26518219080086625 + ], + [ + 0.7441703339623539, + 0.30824544504292245, + -0.26518219080086625 + ], + [ + -0.8054841651698379, + 0.0, + 0.26518219080086625 + ], + [ + 0.8054841651698379, + 0.0, + 0.26518219080086625 + ], + [ + -0.5695633153299774, + -0.5695633153299774, + 0.26518219080086625 + ], + [ + -0.5695633153299774, + 0.5695633153299774, + 0.26518219080086625 + ], + [ + 0.5695633153299774, + -0.5695633153299774, + 0.26518219080086625 + ], + [ + 0.5695633153299774, + 0.5695633153299774, + 0.26518219080086625 + ] + ], + "alternative_name": "Antiprism 8" + }, + "Nonagonal Antiprism": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.7811088185670554, + -0.28430035968124767, + 0.24493217647273668 + ], + [ + -0.7811088185670554, + 0.28430035968124767, + 0.24493217647273668 + ], + [ + 0.7811088185670554, + -0.28430035968124767, + -0.24493217647273668 + ], + [ + 0.7811088185670554, + 0.28430035968124767, + -0.24493217647273668 + ], + [ + -0.8312386426039804, + 0.0, + -0.24493217647273668 + ], + [ + -0.4156193213019902, + -0.7198737811023408, + 0.24493217647273668 + ], + [ + -0.4156193213019902, + 0.7198737811023408, + 0.24493217647273668 + ], + [ + 0.4156193213019902, + -0.7198737811023408, + -0.24493217647273668 + ], + [ + 0.4156193213019902, + 0.7198737811023408, + -0.24493217647273668 + ], + [ + 0.8312386426039804, + 0.0, + 0.24493217647273668 + ], + [ + -0.6367657430725413, + -0.5343099001584961, + -0.24493217647273668 + ], + [ + -0.6367657430725413, + 0.5343099001584961, + -0.24493217647273668 + ], + [ + 0.6367657430725413, + -0.5343099001584961, + 0.24493217647273668 + ], + [ + 0.6367657430725413, + 0.5343099001584961, + 0.24493217647273668 + ], + [ + -0.14434307549451397, + -0.8186102598397438, + -0.24493217647273668 + ], + [ + -0.14434307549451397, + 0.8186102598397438, + -0.24493217647273668 + ], + [ + 0.14434307549451397, + -0.8186102598397438, + 0.24493217647273668 + ], + [ + 0.14434307549451397, + 0.8186102598397438, + 0.24493217647273668 + ] + ], + "alternative_name": "Antiprism 9" + }, + "Decagonal Antiprism": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.8561863955446456, + -0.22816967609975974 + ], + [ + 0.0, + 0.8561863955446456, + -0.22816967609975974 + ], + [ + -0.8561863955446456, + 0.0, + 0.22816967609975974 + ], + [ + 0.8561863955446456, + 0.0, + 0.22816967609975974 + ], + [ + -0.6926693443482491, + -0.5032537365145927, + 0.22816967609975974 + ], + [ + -0.6926693443482491, + 0.5032537365145927, + 0.22816967609975974 + ], + [ + -0.26457614657592626, + -0.8142816506459951, + 0.22816967609975974 + ], + [ + -0.26457614657592626, + 0.8142816506459951, + 0.22816967609975974 + ], + [ + -0.5032537365145927, + -0.6926693443482491, + -0.22816967609975974 + ], + [ + -0.5032537365145927, + 0.6926693443482491, + -0.22816967609975974 + ], + [ + 0.5032537365145927, + -0.6926693443482491, + -0.22816967609975974 + ], + [ + 0.5032537365145927, + 0.6926693443482491, + -0.22816967609975974 + ], + [ + -0.8142816506459951, + -0.26457614657592626, + -0.22816967609975974 + ], + [ + -0.8142816506459951, + 0.26457614657592626, + -0.22816967609975974 + ], + [ + 0.8142816506459951, + -0.26457614657592626, + -0.22816967609975974 + ], + [ + 0.8142816506459951, + 0.26457614657592626, + -0.22816967609975974 + ], + [ + 0.26457614657592626, + -0.8142816506459951, + 0.22816967609975974 + ], + [ + 0.26457614657592626, + 0.8142816506459951, + 0.22816967609975974 + ], + [ + 0.6926693443482491, + -0.5032537365145927, + 0.22816967609975974 + ], + [ + 0.6926693443482491, + 0.5032537365145927, + 0.22816967609975974 + ] + ], + "alternative_name": "Antiprism 10" + }, + "Triangular Prism": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.381571414184444, + -0.6609010760833647, + -0.6609010760833647 + ], + [ + -0.381571414184444, + -0.6609010760833647, + 0.6609010760833647 + ], + [ + -0.381571414184444, + 0.6609010760833647, + -0.6609010760833647 + ], + [ + -0.381571414184444, + 0.6609010760833647, + 0.6609010760833647 + ], + [ + 0.763142828368888, + 0.0, + -0.6609010760833647 + ], + [ + 0.763142828368888, + 0.0, + 0.6609010760833647 + ] + ], + "alternative_name": "Prism 3" + }, + "Square Prism": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.5, + -0.5, + -0.5 + ], + [ + -0.5, + -0.5, + 0.5 + ], + [ + -0.5, + 0.5, + -0.5 + ], + [ + -0.5, + 0.5, + 0.5 + ], + [ + 0.5, + -0.5, + -0.5 + ], + [ + 0.5, + -0.5, + 0.5 + ], + [ + 0.5, + 0.5, + -0.5 + ], + [ + 0.5, + 0.5, + 0.5 + ] + ], + "alternative_name": "Prism 4" + }, + "Pentagonal Prism": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.709907331951114, + 0.0, + -0.41727306021516203 + ], + [ + 0.709907331951114, + 0.0, + 0.41727306021516203 + ], + [ + -0.5743270959798283, + -0.41727306021516203, + -0.41727306021516203 + ], + [ + -0.5743270959798283, + -0.41727306021516203, + 0.41727306021516203 + ], + [ + -0.5743270959798283, + 0.41727306021516203, + -0.41727306021516203 + ], + [ + -0.5743270959798283, + 0.41727306021516203, + 0.41727306021516203 + ], + [ + 0.21937343000427134, + -0.6751619940178137, + -0.41727306021516203 + ], + [ + 0.21937343000427134, + -0.6751619940178137, + 0.41727306021516203 + ], + [ + 0.21937343000427134, + 0.6751619940178137, + -0.41727306021516203 + ], + [ + 0.21937343000427134, + 0.6751619940178137, + 0.41727306021516203 + ] + ], + "alternative_name": "Prism 5" + }, + "Hexagonal Prism": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.7274157573144809, + 0.0, + -0.36370787865724047 + ], + [ + -0.7274157573144809, + 0.0, + 0.36370787865724047 + ], + [ + -0.36370787865724047, + -0.6299605249474366, + -0.36370787865724047 + ], + [ + -0.36370787865724047, + -0.6299605249474366, + 0.36370787865724047 + ], + [ + -0.36370787865724047, + 0.6299605249474366, + -0.36370787865724047 + ], + [ + -0.36370787865724047, + 0.6299605249474366, + 0.36370787865724047 + ], + [ + 0.36370787865724047, + -0.6299605249474366, + -0.36370787865724047 + ], + [ + 0.36370787865724047, + -0.6299605249474366, + 0.36370787865724047 + ], + [ + 0.36370787865724047, + 0.6299605249474366, + -0.36370787865724047 + ], + [ + 0.36370787865724047, + 0.6299605249474366, + 0.36370787865724047 + ], + [ + 0.7274157573144809, + 0.0, + -0.36370787865724047 + ], + [ + 0.7274157573144809, + 0.0, + 0.36370787865724047 + ] + ], + "alternative_name": "Prism 6" + }, + "Heptagonal Prism": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.6753282672910365, + -0.32522095289062963, + -0.32522095289062963 + ], + [ + -0.6753282672910365, + -0.32522095289062963, + 0.32522095289062963 + ], + [ + -0.6753282672910365, + 0.32522095289062963, + -0.32522095289062963 + ], + [ + -0.6753282672910365, + 0.32522095289062963, + 0.32522095289062963 + ], + [ + 0.7495578275232689, + 0.0, + -0.32522095289062963 + ], + [ + 0.7495578275232689, + 0.0, + 0.32522095289062963 + ], + [ + -0.16679230783474383, + -0.7307648478468041, + -0.32522095289062963 + ], + [ + -0.16679230783474383, + -0.7307648478468041, + 0.32522095289062963 + ], + [ + -0.16679230783474383, + 0.7307648478468041, + -0.32522095289062963 + ], + [ + -0.16679230783474383, + 0.7307648478468041, + 0.32522095289062963 + ], + [ + 0.4673416613641457, + -0.5860279074880331, + -0.32522095289062963 + ], + [ + 0.4673416613641457, + -0.5860279074880331, + 0.32522095289062963 + ], + [ + 0.4673416613641457, + 0.5860279074880331, + -0.32522095289062963 + ], + [ + 0.4673416613641457, + 0.5860279074880331, + 0.32522095289062963 + ] + ], + "alternative_name": "Prism 7" + }, + "Octagonal Prism": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + -0.7730278075554669, + -0.29582493470898613 + ], + [ + 0.0, + -0.7730278075554669, + 0.29582493470898613 + ], + [ + 0.0, + 0.7730278075554669, + -0.29582493470898613 + ], + [ + 0.0, + 0.7730278075554669, + 0.29582493470898613 + ], + [ + -0.7730278075554669, + 0.0, + -0.29582493470898613 + ], + [ + -0.7730278075554669, + 0.0, + 0.29582493470898613 + ], + [ + 0.7730278075554669, + 0.0, + -0.29582493470898613 + ], + [ + 0.7730278075554669, + 0.0, + 0.29582493470898613 + ], + [ + -0.54661320476824, + -0.54661320476824, + -0.29582493470898613 + ], + [ + -0.54661320476824, + -0.54661320476824, + 0.29582493470898613 + ], + [ + -0.54661320476824, + 0.54661320476824, + -0.29582493470898613 + ], + [ + -0.54661320476824, + 0.54661320476824, + 0.29582493470898613 + ], + [ + 0.54661320476824, + -0.54661320476824, + -0.29582493470898613 + ], + [ + 0.54661320476824, + -0.54661320476824, + 0.29582493470898613 + ], + [ + 0.54661320476824, + 0.54661320476824, + -0.29582493470898613 + ], + [ + 0.54661320476824, + 0.54661320476824, + 0.29582493470898613 + ] + ], + "alternative_name": "Prism 8" + }, + "Nonagonal Prism": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.748511687878144, + -0.2724359743879986, + -0.2724359743879986 + ], + [ + -0.748511687878144, + -0.2724359743879986, + 0.2724359743879986 + ], + [ + -0.748511687878144, + 0.2724359743879986, + -0.2724359743879986 + ], + [ + -0.748511687878144, + 0.2724359743879986, + 0.2724359743879986 + ], + [ + -0.39827475033917425, + -0.6898321029592598, + -0.2724359743879986 + ], + [ + -0.39827475033917425, + -0.6898321029592598, + 0.2724359743879986 + ], + [ + -0.39827475033917425, + 0.6898321029592598, + -0.2724359743879986 + ], + [ + -0.39827475033917425, + 0.6898321029592598, + 0.2724359743879986 + ], + [ + 0.7965495006783485, + 0.0, + -0.2724359743879986 + ], + [ + 0.7965495006783485, + 0.0, + 0.2724359743879986 + ], + [ + 0.6101923186638455, + -0.5120121495380421, + -0.2724359743879986 + ], + [ + 0.6101923186638455, + -0.5120121495380421, + 0.2724359743879986 + ], + [ + 0.6101923186638455, + 0.5120121495380421, + -0.2724359743879986 + ], + [ + 0.6101923186638455, + 0.5120121495380421, + 0.2724359743879986 + ], + [ + 0.1383193692142985, + -0.7844481239260407, + -0.2724359743879986 + ], + [ + 0.1383193692142985, + -0.7844481239260407, + 0.2724359743879986 + ], + [ + 0.1383193692142985, + 0.7844481239260407, + -0.2724359743879986 + ], + [ + 0.1383193692142985, + 0.7844481239260407, + 0.2724359743879986 + ] + ], + "alternative_name": "Prism 9" + }, + "Decagonal Prism": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.819595660354861, + 0.0, + -0.2532689875656094 + ], + [ + -0.819595660354861, + 0.0, + 0.2532689875656094 + ], + [ + 0.819595660354861, + 0.0, + -0.2532689875656094 + ], + [ + 0.819595660354861, + 0.0, + 0.2532689875656094 + ], + [ + -0.6630668177430399, + -0.4817462419994981, + -0.2532689875656094 + ], + [ + -0.6630668177430399, + -0.4817462419994981, + 0.2532689875656094 + ], + [ + -0.6630668177430399, + 0.4817462419994981, + -0.2532689875656094 + ], + [ + -0.6630668177430399, + 0.4817462419994981, + 0.2532689875656094 + ], + [ + -0.25326898756560945, + -0.7794817935077201, + -0.2532689875656094 + ], + [ + -0.25326898756560945, + -0.7794817935077201, + 0.2532689875656094 + ], + [ + -0.25326898756560945, + 0.7794817935077201, + -0.2532689875656094 + ], + [ + -0.25326898756560945, + 0.7794817935077201, + 0.2532689875656094 + ], + [ + 0.25326898756560945, + -0.7794817935077201, + -0.2532689875656094 + ], + [ + 0.25326898756560945, + -0.7794817935077201, + 0.2532689875656094 + ], + [ + 0.25326898756560945, + 0.7794817935077201, + -0.2532689875656094 + ], + [ + 0.25326898756560945, + 0.7794817935077201, + 0.2532689875656094 + ], + [ + 0.6630668177430399, + -0.4817462419994981, + -0.2532689875656094 + ], + [ + 0.6630668177430399, + -0.4817462419994981, + 0.2532689875656094 + ], + [ + 0.6630668177430399, + 0.4817462419994981, + -0.2532689875656094 + ], + [ + 0.6630668177430399, + 0.4817462419994981, + 0.2532689875656094 + ] + ], + "alternative_name": "Prism 10" + } +} diff --git a/coxeter/families/data/pyramid_dipyramid.json b/coxeter/families/data/pyramid_dipyramid.json new file mode 100644 index 00000000..2e925b42 --- /dev/null +++ b/coxeter/families/data/pyramid_dipyramid.json @@ -0,0 +1,203 @@ +{ + "Triangular Dipyramid": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + 0.0, + -1.3218021521667291 + ], + [ + 0.0, + 0.0, + 1.3218021521667291 + ], + [ + -0.4673276325920336, + -0.8094352034302832, + 0.0 + ], + [ + -0.4673276325920336, + 0.8094352034302832, + 0.0 + ], + [ + 0.9346552651840672, + 0.0, + 0.0 + ] + ], + "alternative_name": "Dipyramid 3" + }, + "Square Dipyramid": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + -0.9085602964160698, + 0.0, + 0.0 + ], + [ + 0.0, + 0.9085602964160698, + 0.0 + ], + [ + 0.0, + 0.0, + -0.9085602964160698 + ], + [ + 0.0, + 0.0, + 0.9085602964160698 + ], + [ + 0.0, + -0.9085602964160698, + 0.0 + ], + [ + 0.9085602964160698, + 0.0, + 0.0 + ] + ], + "alternative_name": "Dipyramid 4" + }, + "Pentagonal Dipyramid": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + 0.0, + -0.6222857864688324 + ], + [ + 0.0, + 0.0, + 0.6222857864688324 + ], + [ + 1.00687955322253, + 0.0, + 0.0 + ], + [ + 0.3111428932344162, + -0.9575993602166403, + 0.0 + ], + [ + 0.3111428932344162, + 0.9575993602166403, + 0.0 + ], + [ + -0.8145826698456813, + -0.5918289522190375, + 0.0 + ], + [ + -0.8145826698456813, + 0.5918289522190375, + 0.0 + ] + ], + "alternative_name": "Dipyramid 5" + }, + "Triangular Pyramid": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + 0.0, + 1.249024766483406 + ], + [ + -0.5887959215002404, + -1.0198244513277526, + -0.41634158882780214 + ], + [ + -0.5887959215002404, + 1.0198244513277526, + -0.41634158882780214 + ], + [ + 1.1775918430004808, + 0.0, + -0.41634158882780214 + ] + ], + "alternative_name": "Pyramid 3" + }, + "Square Pyramid": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + 0.0, + 1.1447142425533319 + ], + [ + 0.0, + -1.1447142425533319, + 0.0 + ], + [ + 0.0, + 1.1447142425533319, + 0.0 + ], + [ + -1.1447142425533319, + 0.0, + 0.0 + ], + [ + 1.1447142425533319, + 0.0, + 0.0 + ] + ], + "alternative_name": "Pyramid 4" + }, + "Pentagonal Pyramid": { + "type": "ConvexPolyhedron", + "vertices": [ + [ + 0.0, + 0.0, + 0.7840309614224682 + ], + [ + 1.268588743813811, + 0.0, + 0.0 + ], + [ + 0.3920154807112341, + -1.2064995913028083, + 0.0 + ], + [ + 0.3920154807112341, + 1.2064995913028083, + 0.0 + ], + [ + -1.0263098526181398, + -0.7456577548379926, + 0.0 + ], + [ + -1.0263098526181398, + 0.7456577548379926, + 0.0 + ] + ], + "alternative_name": "Pyramid 5" + } +} diff --git a/tests/conftest.py b/tests/conftest.py index 00962023..453ef69d 100644 --- a/tests/conftest.py +++ b/tests/conftest.py @@ -7,10 +7,36 @@ from hypothesis.strategies import builds, floats, integers from scipy.spatial import ConvexHull -from coxeter.families import DOI_SHAPE_REPOSITORIES, PlatonicFamily, RegularNGonFamily +from coxeter.families import ( + DOI_SHAPE_REPOSITORIES, + ArchimedeanFamily, + CatalanFamily, + JohnsonFamily, + PlatonicFamily, + PrismAntiprismFamily, + PyramidDipyramidFamily, + RegularNGonFamily, +) from coxeter.shapes import ConvexPolyhedron, ConvexSpheropolyhedron, Polyhedron, Shape2D +# Define a function to combine marks in order to more compactly test shape families +def combine_marks(*marks): + combinedargvalues = [] + combinedids = [] + for mark in marks: + argvalues, ids = mark.kwargs["argvalues"], mark.kwargs["ids"] + combinedargvalues.extend(argvalues) + combinedids.extend(ids) + combined_mark = pytest.mark.parametrize( + argnames="poly", + argvalues=combinedargvalues, + ids=combinedids, + ) + + return combined_mark + + # Need to declare this outside the fixture so that it can be used in multiple # fixtures (pytest does not allow fixtures to be called). def get_cube_points(): @@ -198,6 +224,72 @@ def platonic_solids(): ) +def archimedean_solids(): + """Generate archimedean solids.""" + for shape_name in ArchimedeanFamily.data: + yield ArchimedeanFamily.get_shape(shape_name) + + +# A convenient mark decorator that also includes names for the polyhedra. +# Assumes that the argument name is "poly". +_archimedean_shape_names = ArchimedeanFamily.data.keys() +named_archimedean_mark = pytest.mark.parametrize( + argnames="poly", + argvalues=[ArchimedeanFamily.get_shape(name) for name in _archimedean_shape_names], + ids=_archimedean_shape_names, +) + + +def catalan_solids(): + """Generate catalan solids.""" + for shape_name in CatalanFamily.data: + yield CatalanFamily.get_shape(shape_name) + + +# A convenient mark decorator that also includes names for the polyhedra. +# Assumes that the argument name is "poly". +_catalan_shape_names = CatalanFamily.data.keys() +named_catalan_mark = pytest.mark.parametrize( + argnames="poly", + argvalues=[CatalanFamily.get_shape(name) for name in _catalan_shape_names], + ids=_catalan_shape_names, +) + + +def johnson_solids(): + """Generate johnson solids.""" + for shape_name in JohnsonFamily.data: + yield JohnsonFamily.get_shape(shape_name) + + +# A convenient mark decorator that also includes names for the polyhedra. +# Assumes that the argument name is "poly". +_johnson_shape_names = JohnsonFamily.data.keys() +named_johnson_mark = pytest.mark.parametrize( + argnames="poly", + argvalues=[JohnsonFamily.get_shape(name) for name in _johnson_shape_names], + ids=_johnson_shape_names, +) + +_prismantiprism_shape_names = PrismAntiprismFamily.data.keys() +named_prismantiprism_mark = pytest.mark.parametrize( + argnames="poly", + argvalues=[ + PrismAntiprismFamily.get_shape(name) for name in _prismantiprism_shape_names + ], + ids=_prismantiprism_shape_names, +) + +_pyramiddipyramid_shape_names = PyramidDipyramidFamily.data.keys() +named_pyramiddipyramid_mark = pytest.mark.parametrize( + argnames="poly", + argvalues=[ + PyramidDipyramidFamily.get_shape(name) for name in _pyramiddipyramid_shape_names + ], + ids=_pyramiddipyramid_shape_names, +) + + def regular_polygons(n=10): """Generate regular polygons.""" for i in range(3, n + 1): @@ -234,3 +326,15 @@ def _test_get_set_minimal_bounding_sphere_radius(shape, centered=False): for shape_id in _damasceno_shape_names ], ) + +data_filenames_mark = pytest.mark.parametrize( + argnames="family", + argvalues=[ + "platonic", + "archimedean", + "catalan", + "johnson", + "prism_antiprism", + "pyramid_dipyramid", + ], +) diff --git a/tests/test_polyhedron.py b/tests/test_polyhedron.py index c4c32b02..7a2adcc5 100644 --- a/tests/test_polyhedron.py +++ b/tests/test_polyhedron.py @@ -16,10 +16,16 @@ EllipsoidSurfaceStrategy, Random3DRotationStrategy, _test_get_set_minimal_bounding_sphere_radius, + combine_marks, get_oriented_cube_faces, get_oriented_cube_normals, + named_archimedean_mark, + named_catalan_mark, named_damasceno_shapes_mark, + named_johnson_mark, named_platonic_mark, + named_prismantiprism_mark, + named_pyramiddipyramid_mark, sphere_isclose, ) from coxeter.families import DOI_SHAPE_REPOSITORIES, PlatonicFamily @@ -149,6 +155,44 @@ def test_volume_damasceno_shapes(shape): assert np.isclose(poly.volume, hull.volume) +@named_damasceno_shapes_mark +def test_surface_area_damasceno_shapes(shape): + if shape["name"] in ("RESERVED", "Sphere"): + return + vertices = shape["vertices"] + poly = ConvexPolyhedron(vertices) + hull = ConvexHull(vertices) + assert np.isclose(poly.surface_area, hull.area) + + +@combine_marks( + named_platonic_mark, + named_archimedean_mark, + named_catalan_mark, + named_johnson_mark, + named_prismantiprism_mark, + named_pyramiddipyramid_mark, +) +def test_volume_shapes(poly): + vertices = poly.vertices + hull = ConvexHull(vertices) + assert np.isclose(poly.volume, hull.volume) + + +@combine_marks( + named_platonic_mark, + named_archimedean_mark, + named_catalan_mark, + named_johnson_mark, + named_prismantiprism_mark, + named_pyramiddipyramid_mark, +) +def test_surface_area_shapes(poly): + vertices = poly.vertices + hull = ConvexHull(vertices) + assert np.isclose(poly.surface_area, hull.area) + + # This test is a bit slow (a couple of minutes), so skip running it locally. @pytest.mark.skipif( os.getenv("CI", "false") != "true" and os.getenv("CIRCLECI", "false") != "true", @@ -308,8 +352,8 @@ def test_curvature(): for name, curvature in known_shapes.items(): poly = PlatonicFamily.get_shape(name) - if name == "Dodecahedron": - poly.merge_faces(rtol=1) + # Normalize volume to ensure known_shape data is accurate + poly.volume = 1 assert np.isclose(poly.mean_curvature, curvature) @@ -339,8 +383,9 @@ def test_asphericity(): pass -@named_platonic_mark -def test_circumsphere_platonic(poly): +# Circumspheres cannot be generated for some Johnson and Catalan solids +@combine_marks(named_platonic_mark, named_archimedean_mark) +def test_circumsphere(poly): circumsphere = poly.circumsphere # Ensure polyhedron is centered, then compute distances. @@ -350,8 +395,8 @@ def test_circumsphere_platonic(poly): assert np.allclose(r2, circumsphere.radius**2) -@named_platonic_mark -def test_circumsphere_radius_platonic(poly): +@combine_marks(named_platonic_mark, named_archimedean_mark) +def test_circumsphere_radius(poly): # Ensure polyhedron is centered, then compute distances. poly.center = [0, 0, 0] r2 = np.sum(poly.vertices**2, axis=1) @@ -417,14 +462,16 @@ def testfun(center, points, shape_index): testfun() -@named_platonic_mark -def test_bounding_sphere_platonic(poly): +# Shapes where |aspect ratio - 1| >> 0 cannot pass this test: this includes many +# Johnson solids. Shapes with large numbers of vertices also tend to fail +@combine_marks(named_platonic_mark, named_archimedean_mark) +def test_bounding_sphere(poly): # Ensure polyhedron is centered, then compute distances. poly.center = [0, 0, 0] r2 = np.sum(poly.vertices**2, axis=1) bounding_sphere = poly.minimal_bounding_sphere - assert np.allclose(r2, bounding_sphere.radius**2, rtol=1e-4) + assert np.allclose(r2, bounding_sphere.radius**2, rtol=1e-5) with pytest.deprecated_call(): assert sphere_isclose(bounding_sphere, poly.bounding_sphere) @@ -477,20 +524,40 @@ def test_maximal_centered_bounded_sphere_convex_hulls(points, test_points): assert sphere_isclose(insphere, poly.insphere_from_center) +# Platonic and Catalan shapes have a centered insphere, but Archimedean +# and Johnson solids do not. @named_platonic_mark -def test_insphere(poly): +def test_insphere_platonic(poly): # The insphere should be centered for platonic solids. poly_insphere = poly.insphere assert sphere_isclose( - poly_insphere, poly.maximal_centered_bounded_sphere, atol=1e-4 + poly_insphere, poly.maximal_centered_bounded_sphere, atol=1e-5 ) # The insphere of a platonic solid should be rotation invariant. - @settings(deadline=300) + @settings(deadline=500) + @given(Random3DRotationStrategy) + def check_rotation_invariance(quat): + rotated_poly = ConvexPolyhedron(rowan.rotate(quat, poly.vertices)) + assert sphere_isclose(poly_insphere, rotated_poly.insphere, atol=1e-5) + + check_rotation_invariance() + + +@named_catalan_mark +def test_insphere_catalan(poly): + # The insphere should be centered for catalan solids. + poly_insphere = poly.insphere + assert sphere_isclose( + poly_insphere, poly.maximal_centered_bounded_sphere, atol=1e-5 + ) + + # The insphere of a catalan solid should be rotation invariant. + @settings(deadline=1200) @given(Random3DRotationStrategy) def check_rotation_invariance(quat): rotated_poly = ConvexPolyhedron(rowan.rotate(quat, poly.vertices)) - assert sphere_isclose(poly_insphere, rotated_poly.insphere, atol=1e-4) + assert sphere_isclose(poly_insphere, rotated_poly.insphere, atol=1e-5) check_rotation_invariance() @@ -499,6 +566,7 @@ def test_rotate_inertia(tetrahedron): # Use the input as noise rather than the base points to avoid precision and # degenerate cases provided by hypothesis. tet = PlatonicFamily.get_shape("Tetrahedron") + tet.volume = 1 @given( arrays(np.float64, (4, 3), elements=floats(-10, 10, width=64), unique=True), @@ -636,12 +704,26 @@ def test_form_factor(cube): ) -@named_platonic_mark +@combine_marks( + named_platonic_mark, + named_archimedean_mark, + named_catalan_mark, + named_johnson_mark, + named_prismantiprism_mark, + named_pyramiddipyramid_mark, +) def test_get_set_minimal_bounding_sphere_radius(poly): _test_get_set_minimal_bounding_sphere_radius(poly) -@named_platonic_mark +@combine_marks( + named_platonic_mark, + named_archimedean_mark, + named_catalan_mark, + named_johnson_mark, + named_prismantiprism_mark, + named_pyramiddipyramid_mark, +) def test_get_set_minimal_centered_bounding_sphere_radius(poly): _test_get_set_minimal_bounding_sphere_radius(poly, True) diff --git a/tests/test_shape_getters.py b/tests/test_shape_getters.py index 9d56bb7d..32783eb9 100644 --- a/tests/test_shape_getters.py +++ b/tests/test_shape_getters.py @@ -1,10 +1,14 @@ # Copyright (c) 2021 The Regents of the University of Michigan # All rights reserved. # This software is licensed under the BSD 3-Clause License. +import json + import numpy as np from pytest import approx +from conftest import data_filenames_mark from coxeter import from_gsd_type_shapes +from coxeter.families import common def test_gsd_shape_getter(): @@ -96,3 +100,23 @@ def test_gsd_shape_getter(): # Now convert back and make sure the conversion is lossless. assert shape.gsd_shape_spec == shape_spec + + +@data_filenames_mark +def test_json_data_families(family): + # Iterate through shape families stored in common + for fam in [attr for attr in dir(common)]: + # Set correct shape family for current test + if family.title().replace("_", "") in fam: + # Load the family via common + module = getattr(common, fam) + # Manually load the json data + with open("coxeter/families/data/" + family + ".json") as file: + fam_data = json.load(file) + + # Extract the stored shape keys + shapes = list(fam_data.keys()) + for shape in shapes: + module_vertices = module.get_shape(shape).vertices + json_vertices = fam_data[shape]["vertices"] + assert np.all(module_vertices == json_vertices)