http://debianws.lexgopc.com/wiki143/index.php?action=history&feed=atom&title=Compound_of_five_truncated_cubes Compound of five truncated cubes - Revision history 2026-05-10T22:26:10Z Revision history for this page on the wiki MediaWiki 1.43.1 http://debianws.lexgopc.com/wiki143/index.php?title=Compound_of_five_truncated_cubes&diff=5950005&oldid=prev imported>Eancheta8352664: name + truncation 2025-06-24T19:52:33Z <p>name + truncation</p> <p><b>New page</b></p><div>{{Short description|Polyhedral compound}}<br /> {| class=wikitable style=&quot;float:right; margin-left:8px; width:250px&quot;<br /> !bgcolor=#e7dcc3 colspan=2|Compound of five truncated cubes<br /> |-<br /> |align=center colspan=2|[[Image:UC57-5 truncated cubes.png|200px]]<br /> |-<br /> |bgcolor=#e7dcc3|Type||[[Uniform polyhedron compound|Uniform compound]]<br /> |-<br /> |bgcolor=#e7dcc3|Index||UC&lt;sub&gt;57&lt;/sub&gt;<br /> |-<br /> |bgcolor=#e7dcc3|Polyhedra||5 [[truncated cube]]s<br /> |-<br /> |bgcolor=#e7dcc3|Faces||40 [[triangles]], 30 [[octagons]]<br /> |-<br /> |bgcolor=#e7dcc3|Edges||180<br /> |-<br /> |bgcolor=#e7dcc3|Vertices||120<br /> |-<br /> |bgcolor=#e7dcc3|[[Symmetry group]]||[[Icosahedral symmetry|icosahedral]] (&#039;&#039;I&lt;sub&gt;h&lt;/sub&gt;&#039;&#039;)<br /> |-<br /> |bgcolor=#e7dcc3|[[Subgroup]] restricting to one constituent||[[Tetrahedral symmetry|pyritohedral]] (&#039;&#039;T&lt;sub&gt;h&lt;/sub&gt;&#039;&#039;)<br /> |}<br /> This [[uniform polyhedron compound]] is a composition of 5 [[truncated cube]]s, formed by [[Truncation (geometry)|truncating]] each of the cubes in the [[compound of five cubes|compound of 5 cubes]]. It is also called the truncated rhombihedron.<br /> <br /> == Cartesian coordinates ==<br /> [[Cartesian coordinates]] for the vertices of this compound are all the cyclic permutations of<br /> <br /> : (±(2+{{radic|2}}), ±{{radic|2}}, ±(2+{{radic|2}}))<br /> : (±τ, ±(τ&lt;sup&gt;−1&lt;/sup&gt;+τ&lt;sup&gt;−1&lt;/sup&gt;{{radic|2}}), ±(2τ−1+τ{{radic|2}}))<br /> : (±1, ±(τ&lt;sup&gt;−2&lt;/sup&gt;−τ&lt;sup&gt;−1&lt;/sup&gt;{{radic|2}}), ±(τ&lt;sup&gt;2&lt;/sup&gt;+τ{{radic|2}}))<br /> : (±(1+{{radic|2}}), ±(−τ&lt;sup&gt;−2&lt;/sup&gt;−{{radic|2}}), ±(τ&lt;sup&gt;2&lt;/sup&gt;+{{radic|2}}))<br /> : (±(τ+τ{{radic|2}}), ±(−τ&lt;sup&gt;−1&lt;/sup&gt;), ±(2τ−1+τ&lt;sup&gt;−1&lt;/sup&gt;{{radic|2}}))<br /> <br /> where τ = (1+{{radic|5}})/2 is the [[golden ratio]] (sometimes written φ).<br /> <br /> == References ==<br /> *{{citation|first=John|last=Skilling|title=Uniform Compounds of Uniform Polyhedra|journal=[[Mathematical Proceedings of the Cambridge Philosophical Society]]|volume=79|issue=3|pages=447–457|year=1976|doi=10.1017/S0305004100052440|bibcode=1976MPCPS..79..447S |mr=0397554|s2cid=123279687 }}.<br /> * {{cite web |last=McCooey |first=Robert |title=Uniform Polyhedron Compounds |url=http://www.polytope.net/hedrondude/comptrunc.htm |website=Hedron Dude |access-date=24 June 2025}}<br /> <br /> [[Category:Polyhedral compounds]]<br /> <br /> <br /> {{polyhedron-stub}}</div> imported>Eancheta8352664