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Data of coordinates of all regular-faced convex polyhedra Jun. 22, 1994 Kobayasi, Mituo Department of Computer Science and Information Mathematics University of Electro-Communications 1-5-1, Chofugaoka, Chofu-shi, Tokyo 182, JAPAN Suzuki, Takuzi Department of Museum Science National Museum of Japanese History 117, Jyonai-cho, Sakura-shi, Chiba 285, JAPAN E-mail: [email protected] [email protected] 1. Introduction Regular polyhedron, semiregular polyhedron, prism, and antiprism are kinds of convex polyhedra with regular faces. Viktor A. Zalgaller proved that the number of kinds of other convex polyhedra with regular faces is 92[1]. They have beautiful exterior, but unfortunately not familiar. We devised a set of algorithms to calculate coordinates of all vertices of a given convex polyhedron with regular faces[2]. Presented here is the data of adjacency list and coordinates of vertices of every regular-faced convex polyhedron. Notes: [1] Zalgaller,V.A.: Convex Polyhedra with Regular Faces, Consultants Bureau, 1969. (Zalgaller,B.A.: Vypuklye Mnogogranniki c Pravil'nymi Granyami, Nauka Press, 1966.) [2] Kobayasi,M. and Suzuki,T.: Calculation of Coordinates of Vertices of All Convex Polyhedra with Regular Faces (written in Japanese), Bulletin of The University of Electro-Communications, Vol.5, No.2, pp.147-184(1992). 2. Data Files Data files of coordinates exist in the directory `data/.' One file contains the data of one polyhedron. The following list shows file names of each polyhedron. The correspondence of file names and names of polyhedron is given in Table 1, Table 2, and Table 3, which exist in the file `dname.tex.' The letter L and R respectively denote the left-hand and the right-hand of the polyhedron. Regular polyhedra: r01, r02, r03, r04, r05. (r02 = a03, r03 = p04) Semiregular polyhedra: s01, s02, s03, s04, s05, s06, s07, s08, s09, s10, s11, s12L, s12R, s13L, s13R. (n37 is a so-called 'Mirror's polyhedron,' and sometimes classified as a kind of semiregular polyhedron.) Prism: p03, p04, p05, p06, p07, p08, p09, p10. Antiprisms: a03, a04, a05, a06, a07, a08, a09, a10. Other regular-faced convex polyhedra: n01, n02, n03, n04, n05, n06, n07, n08, n09, n10, n11, n12, n13, n14, n15, n16, n17, n18, n19, n20, n21, n22, n23, n24, n25, n26, n27, n28, n29, n30, n31, n32, n33, n34, n35, n36, n37, n38, n39, n40, n41, n42, n43, n44L, n44R, n45L, n45R, n46L, n46R, n47L, n47R, n48L, n48R, n49, n50, n51, n52, n53, n54, n55, n56, n57, n58, n59, n60, n61, n62, n63, n64, n65, n66, n67, n68, n69, n70, n71, n72, n73, n74, n75, n76, n77, n78, n79, n80, n81, n82, n83, n84, n85, n86, n87, n88, n89, n90, n91, n92. 3. The Data Format The data of one polyhedron consists of 4 parts: 1. Adjacency list of vertices. 2. List of faces around each vertices. 3. List of vertices of each faces. 4. Coordinates of each vertices. Every vertex and Every face is identified by a number. For n vertices, the identifier runs from 1 to n. For m faces, the identifier runs from 1 to m. Following is the data format of a polyhedron: # of vertices ID of vertex, # of adjacent vertices, ID list of adjacent vertices ... # of vertices ID of vertex, # of adjacent faces, ID list of adjacent faces ... # of faces ID of face, # of vertices of the face, ID list of vertices of the face ... # of vertices ID of vertex, X-coordinate, Y-coordinate, Z-coordinate ... 4. Hardcopy Hardcopy files of exterior of polyhedra are given in the directory `hardcopy/.' The format is PBM.