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sample-crawled-page-type-3.txt
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<!doctype html>
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<title>Quasirhombicuboctahedron -- from Wolfram MathWorld</title>
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<meta name="DC.Creator" content="Weisstein, Eric W." />
<meta name="DC.Description" content="The quasirhombicuboctahedron is the name given by Wenninger (1989, p. 132) to the uniform polyhedron with Maeder index 17 (Maeder 1997), Wenninger index 85 (Wenninger 1989), Coxeter index 59 (Coxeter et al. 1954), Har'El index 22 (Har'El 1993), faces 18{4}+8{3/2}, Schläfli symbol r'{3/4}, and Wythoff symbol 3/24|2. Unfortunately, other authors (e.g., Maeder 1997) use the term "great rhombicuboctahedron" to refer to this solid, despite the fact that "'great..." />
<meta name="description" content="The quasirhombicuboctahedron is the name given by Wenninger (1989, p. 132) to the uniform polyhedron with Maeder index 17 (Maeder 1997), Wenninger index 85 (Wenninger 1989), Coxeter index 59 (Coxeter et al. 1954), Har'El index 22 (Har'El 1993), faces 18{4}+8{3/2}, Schläfli symbol r'{3/4}, and Wythoff symbol 3/24|2. Unfortunately, other authors (e.g., Maeder 1997) use the term "great rhombicuboctahedron" to refer to this solid, despite the fact that "'great..." />
<meta name="DC.Date.Modified" scheme="W3CDTF" content="2002-12-03" />
<meta name="DC.Date.Modified" scheme="W3CDTF" content="2023-08-28" />
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<meta property="og:title" content="Quasirhombicuboctahedron -- from Wolfram MathWorld">
<meta property="og:description" content="The quasirhombicuboctahedron is the name given by Wenninger (1989, p. 132) to the uniform polyhedron with Maeder index 17 (Maeder 1997), Wenninger index 85 (Wenninger 1989), Coxeter index 59 (Coxeter et al. 1954), Har'El index 22 (Har'El 1993), faces 18{4}+8{3/2}, Schläfli symbol r'{3/4}, and Wythoff symbol 3/24|2. Unfortunately, other authors (e.g., Maeder 1997) use the term "great rhombicuboctahedron" to refer to this solid, despite the fact that "'great...">
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<meta name="twitter:description" content="The quasirhombicuboctahedron is the name given by Wenninger (1989, p. 132) to the uniform polyhedron with Maeder index 17 (Maeder 1997), Wenninger index 85 (Wenninger 1989), Coxeter index 59 (Coxeter et al. 1954), Har'El index 22 (Har'El 1993), faces 18{4}+8{3/2}, Schläfli symbol r'{3/4}, and Wythoff symbol 3/24|2. Unfortunately, other authors (e.g., Maeder 1997) use the term "great rhombicuboctahedron" to refer to this solid, despite the fact that "'great...">
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<!-- Begin Title -->
<h1>Quasirhombicuboctahedron</h1>
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<a href="/notebooks/Polyhedra/Quasirhombicuboctahedron.nb" download="Quasirhombicuboctahedron.nb"><img src="/images/entries/download-notebook-icon.png" width="26" height="27" alt="DOWNLOAD Mathematica Notebook" /><span>Download
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<img style="max-width:100%;max-height:100%;" width="219.681" height="221.9" src="images/eps-svg/U17_700.svg"
class="center-image" alt="U17" />
<p>
The quasirhombicuboctahedron is the name given by Wenninger (1989, p. 132) to the <a href="/UniformPolyhedron.html">uniform polyhedron</a> with Maeder index
17 (Maeder 1997), Wenninger index 85 (Wenninger 1989), Coxeter index 59 (Coxeter
<i>et al. </i>1954), Har'El index 22 (Har'El 1993), faces <img src="/images/equations/Quasirhombicuboctahedron/Inline1.svg"
class="inlineformula" style="max-height:100%;max-width:100%" border="0" width="116"
height="21" alt="18{4}+8{3/2}" />, <a href="/SchlaefliSymbol.html">Schläfli
symbol</a> r'<img src="/images/equations/Quasirhombicuboctahedron/Inline2.svg" class="inlineformula"
style="max-height:100%;max-width:100%" border="0" width="24" height="27" alt="{3/4}" />,
and <a href="/WythoffSymbol.html">Wythoff symbol</a> <img src="/images/equations/Quasirhombicuboctahedron/Inline3.svg"
class="inlineformula" style="max-height:100%;max-width:100%" border="0" width="46"
height="27" alt="3/24|2" />.
</p>
<p>
Unfortunately, other authors (e.g., Maeder 1997) use the term "<a href="/GreatRhombicuboctahedron.html">great rhombicuboctahedron</a>" to refer to this solid, despite the fact that "'<a
href="/GreatRhombicuboctahedron.html">great rhombicuboctahedron</a>" is commonly
used to refer to a distinct (and more common) <a href="/ArchimedeanSolid.html">Archimedean
solid</a> (Cundy and Rowlett 1989, p. 106).
</p>
<p>
The quasirhombicuboctahedron is implemented in the <a href="http://www.wolfram.com/language/">Wolfram Language</a> as <tt><a href="http://reference.wolfram.com/language/ref/UniformPolyhedron.html">UniformPolyhedron</a></tt>[85],
<tt><a href="http://reference.wolfram.com/language/ref/UniformPolyhedron.html">UniformPolyhedron</a></tt>[<tt>"GreatRhombicuboctahedron"</tt>],
<tt><a href="http://reference.wolfram.com/language/ref/UniformPolyhedron.html">UniformPolyhedron</a></tt>[<img
src="/images/equations/Quasirhombicuboctahedron/Inline4.svg" class="inlineformula"
style="max-height:100%;max-width:100%" border="0" width="6" height="21" alt="{" /><tt>"Coxeter"</tt>,
59<img src="/images/equations/Quasirhombicuboctahedron/Inline5.svg" class="inlineformula"
style="max-height:100%;max-width:100%" border="0" width="6" height="21" alt="}" />],
<tt><a href="http://reference.wolfram.com/language/ref/UniformPolyhedron.html">UniformPolyhedron</a></tt>[<img
src="/images/equations/Quasirhombicuboctahedron/Inline6.svg" class="inlineformula"
style="max-height:100%;max-width:100%" border="0" width="6" height="21" alt="{" /><tt>"Kaleido"</tt>,
22<img src="/images/equations/Quasirhombicuboctahedron/Inline7.svg" class="inlineformula"
style="max-height:100%;max-width:100%" border="0" width="6" height="21" alt="}" />],
<tt><a href="http://reference.wolfram.com/language/ref/UniformPolyhedron.html">UniformPolyhedron</a></tt>[<img
src="/images/equations/Quasirhombicuboctahedron/Inline8.svg" class="inlineformula"
style="max-height:100%;max-width:100%" border="0" width="6" height="21" alt="{" /><tt>"Uniform"</tt>,
17<img src="/images/equations/Quasirhombicuboctahedron/Inline9.svg" class="inlineformula"
style="max-height:100%;max-width:100%" border="0" width="6" height="21" alt="}" />],
or <tt><a href="http://reference.wolfram.com/language/ref/UniformPolyhedron.html">UniformPolyhedron</a></tt>[<img
src="/images/equations/Quasirhombicuboctahedron/Inline10.svg" class="inlineformula"
style="max-height:100%;max-width:100%" border="0" width="6" height="21" alt="{" /><tt>"Wenninger"</tt>,
85<img src="/images/equations/Quasirhombicuboctahedron/Inline11.svg" class="inlineformula"
style="max-height:100%;max-width:100%" border="0" width="6" height="21" alt="}" />].
It will also be implemented in a future version of the <a href="http://www.wolfram.com/language/">Wolfram
Language</a> as <tt><a href="http://reference.wolfram.com/language/ref/PolyhedronData.html">PolyhedronData</a></tt>[<tt>"Quasirhombicuboctahedron"</tt>].
</p>
<img style="max-width:100%;max-height:100%;" width="201.853" height="201.853" src="images/eps-svg/SmallRhombicuboctahedralGraph_800.svg"
class="center-image" alt="SmallRhombicuboctahedralGraph" />
<p>
The <a href="/Skeleton.html">skeleton</a> of the quasirhombicuboctahedron is the <a href="/SmallRhombicuboctahedralGraph.html">small rhombicuboctahedral graph</a>,
illustrated above.
</p>
<p>
The <a href="/DualPolyhedron.html">dual</a> of the quasirhombicuboctahedron is the <a href="/GreatDeltoidalIcositetrahedron.html">great deltoidal icositetrahedron</a>.
</p>
<p>
Its <a href="/Circumradius.html">circumradius</a> for unit edge length is
</p>
<div>
<table summary="" width="100%" align="center" cellspacing="0" cellpadding="0" style="padding-left: 50px">
<tr><td align="left"><img src="/images/equations/Quasirhombicuboctahedron/NumberedEquation1.svg" class="numberedequation" style="max-height:100%;max-width:100%" border="0" width="134"
height="31" alt=" R=1/2sqrt(5-2sqrt(2)). " /></td></tr>
</table>
</div>
<img style="max-width:100%;max-height:100%;" width="352.821" height="167.257" src="images/eps-svg/U17Hull_700.svg"
class="center-image" alt="U17Hull" />
<p>
The <a href="/ConvexHull.html">convex hull</a> of the quasirhombicuboctahedron is the Archimedean <a href="/TruncatedCube.html">truncated cube</a>, whose dual is the
<a href="/SmallTriakisOctahedron.html">small triakis octahedron</a>, so the dual
of the quasirhombicuboctahedron (i.e., the <a href="/GreatDeltoidalIcositetrahedron.html">great
deltoidal icositetrahedron</a>) is one of the stellations of the <a href="/SmallTriakisOctahedron.html">small
triakis octahedron</a> (Wenninger 1983, p. 57).
</p>
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<h2>See also</h2><a href="/GreatRhombicuboctahedron.html">Great Rhombicuboctahedron</a>,
<a href="/UniformPolyhedron.html">Uniform Polyhedron</a>
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<h2>References</h2><cite>Coxeter, H. S. M.; Longuet-Higgins, M. S.; and Miller, J. C. P. "Uniform Polyhedra." <i>Phil. Trans. Roy.
Soc. London Ser. A</i> <b>246</b>, 401-450, 1954.</cite><cite>Cundy, H. and Rollett,
A. "Great Rhombicuboctahedron or Truncated Cuboctahedron. <img src="/images/equations/Quasirhombicuboctahedron/Inline12.svg"
class="inlineformula" style="max-height:100%;max-width:100%" border="0" width="41"
height="21" alt="4.6.8" />." §3.7.6 in <i><a href="http://www.amazon.com/exec/obidos/ASIN/0906212200/ref=nosim/ericstreasuretro">Mathematical
Models, 3rd ed.</a></i> Stradbroke, England: Tarquin Pub., p. 106, 1989.</cite><cite>Har'El,
Z. "Uniform Solution for Uniform Polyhedra." <i>Geometriae Dedicata</i> <b>47</b>,
57-110, 1993.</cite><cite>Maeder, R. E. "17: Great Rhombicuboctahedron."
1997. <a href="https://www.mathconsult.ch/static/unipoly/17.html">https://www.mathconsult.ch/static/unipoly/17.html</a>.</cite><cite>Wenninger,
M. J. <i><a href="http://www.amazon.com/exec/obidos/ASIN/0521245249/ref=nosim/ericstreasuretro">Dual
Models.</a></i> Cambridge, England: Cambridge University Press, pp. 57 and 59,
1983.</cite><cite>Wenninger, M. J. "Quasirhombicuboctahedron." Model
85 in <i><a href="http://www.amazon.com/exec/obidos/ASIN/0521098599/ref=nosim/ericstreasuretro">Polyhedron
Models.</a></i> Cambridge, England: Cambridge University Press, pp. 132-133,
1989.</cite>
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<p>
<a href="/about/author.html">Weisstein, Eric W.</a> "Quasirhombicuboctahedron."
From <a href="/"><i>MathWorld</i></a>--A Wolfram Web Resource. <a href="https://mathworld.wolfram.com/Quasirhombicuboctahedron.html">https://mathworld.wolfram.com/Quasirhombicuboctahedron.html</a>
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