Small complex icosidodecahedron

<h2 id="as-a-compound">As a compound</h2>
<p>The small complex icosidodecahedron can be seen as a <a href="/facts/Polyhedron_compound/L13pItNN">compound</a> of the <a href="/facts/Icosahedron/wWbpnDYp">icosahedron</a> {3,5} and the <a href="/facts/Great_dodecahedron/LWt3Hgg4">great dodecahedron</a> {5,5/2} where all vertices are precise and edges coincide. The small complex icosidodecahedron resembles an icosahedron, because the great dodecahedron is completely contained inside the icosahedron.
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Compound polyhedron<table><tbody><tr><td></td><td></td><td></td></tr><tr><td><a href="/facts/Icosahedron/wWbpnDYp">Icosahedron</a></td><td><a href="/facts/Great_dodecahedron/LWt3Hgg4">Great dodecahedron</a></td><td>Compound</td></tr></tbody></table>
<p>Its two-dimensional analogue would be the compound of a regular <a href="/facts/Pentagon/xoq5oJeQ">pentagon</a>, {5}, representing the icosahedron as the <i>n</i>-dimensional <a href="/facts/Pentagonal_polytope/4uxePdKt">pentagonal polytope</a>, and regular <a href="/facts/Pentagram/cN0ke8tp">pentagram</a>, {5/2}, as the <i>n</i>-dimensional star. These shapes would share vertices, similarly to how its 3D equivalent shares edges.
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Compound polygon<table><tbody><tr><td></td><td></td><td></td></tr><tr><td><a href="/facts/Pentagon/xoq5oJeQ">Pentagon</a></td><td><a href="/facts/Pentagram/cN0ke8tp">Pentagram</a></td><td>Compound</td></tr></tbody></table>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Great_complex_icosidodecahedron/pEPjw0sf">Great complex icosidodecahedron</a></li></ul>

<ul><li><a href="/facts/Harold_Scott_MacDonald_Coxeter/D2l5jWGG">Coxeter, Harold Scott MacDonald</a>; Longuet-Higgins, M. S.; Miller, J. C. P. (1954), "Uniform polyhedra", <i>Philosophical Transactions of the Royal Society of London. Series A. Mathematical and Physical Sciences</i>, 246 (916): 401–450, <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/1954RSPTA.246..401C">1954RSPTA.246..401C</a>, <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1098%2Frsta.1954.0003">10.1098/rsta.1954.0003</a>, <a href="/facts/ISSN_(identifier)/DPAflDvU">ISSN</a> <a href="https://search.worldcat.org/issn/0080-4614">0080-4614</a>, <a href="/facts/JSTOR_(identifier)/YTeVmaJ7">JSTOR</a> <a href="https://www.jstor.org/stable/91532">91532</a>, <a href="/facts/MR_(identifier)/uP137L11">MR</a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=0062446">0062446</a>, <a href="/facts/S2CID_(identifier)/ldJsHa2Y">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:202575183">202575183</a> (Table 6, degenerate cases)</li>
<li><a href="/facts/Eric_W._Weisstein/FbMuVDep">Weisstein, Eric W.</a> <a href="https://mathworld.wolfram.com/SmallComplexIcosidodecahedron.html">"Small complex icosidodecahedron"</a>. <i><a href="/facts/MathWorld/yc1jodbq">MathWorld</a></i>.</li>
<li>Klitzing, Richard. <a href="https://bendwavy.org/klitzing/dimensions/polyhedra-neu.htm">"3D uniform polyhedra x3/2o5o5*a - cid"</a>.</li></ul>

Small complex icosidodecahedron open-in-new

Small complex icosidodecahedron