View source for Rho Geminorum

{| class="wikitable" align="right" style="margin-left:10px" width="250"
!bgcolor=#e7dcc3 colspan=2|Triakis truncated tetrahedral honeycomb
|-
|bgcolor=#ffffff align=center colspan=2|[[File:Triakis truncated tetrahedral honeycomb.jpg|280px]]
|-
|bgcolor=#e7dcc3|Cell type||[[Triakis truncated tetrahedron]]
|-
|bgcolor=#e7dcc3|Face types||[[hexagon]]<BR>[[isosceles triangle]]
|-
|bgcolor=#e7dcc3|[[Coxeter group]]||<math>{\tilde{A}}_3</math>×2, [<span/>[3<sup>[4]</sup>]] (double)
|-
|bgcolor=#e7dcc3|[[Space group]]||Fd{{overline|3}}m (227)
|-
|}
The '''triakis truncated tetrahedral honeycomb''' is a space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]) in [[Euclidean 3-space]] made up of [[triakis truncated tetrahedron|triakis truncated tetrahedra]]. It was discovered in 1914.<ref>{{cite journal|first1=L.|last1=Föppl|year=1914|title=Der Fundamentalbereich des Diamantgitters|journal=Phys. Zeitschr.|volume=15|pages=191–193}}</ref><ref>{{cite journal|last1=Grünbaum|first1=B.|last2=Shephard|first2=G. C.|title=Tilings with Congruent Tiles|journal=Bull. Amer. Math. Soc.|volume=3|pages=951–973|year=1980|url=http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.bams/1183547682}}</ref>

It can be seen as the uniform [[quarter cubic honeycomb]] where its [[tetrahedron|tetrahedal]] cells are subdivided by the center point into 4 shorter tetrahedra, and each adjoined to the adjacent truncated tetrahedral cells.

It is the [[Voronoi tessellation]] of the [[carbon]] atoms in [[diamond]],<ref name=conway2003>{{cite web|last=Conway|first=John|title=Voronoi Polyhedron|url=https://groups.google.com/forum/?fromgroups=#!msg/geometry.puzzles/pkL3avbWPoc/ABSaqdQaqu4J|work=geometry.puzzles|accessdate=20 September 2012}}</ref><ref name=conway2008>{{cite book|last1=Conway|first1=John H.|last2=Burgiel|first2=Heidi|last3=Goodman-Strauss|first3=Chaim|title=The Symmetries of Things|page=332|year=2008|isbn=1568812205}}</ref> which lie in the [[diamond cubic]] crystal structure.

Being composed entirely of [[triakis truncated tetrahedron|triakis truncated tetrahedra]], it is [[cell-transitive]].

==See also==
*[[Disphenoid tetrahedral honeycomb]]

==References==
{{reflist}}

[[Category:Honeycombs (geometry)]]


{{Polychora-stub}}