View source for Quarter 6-cubic honeycomb

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!bgcolor=#e7dcc3 colspan=2|quarter 6-cubic honeycomb
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|bgcolor=#ffffff align=center colspan=2|(No image)
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|bgcolor=#e7dcc3|Type||Uniform 6-honeycomb
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|bgcolor=#e7dcc3|Family||[[Quarter hypercubic honeycomb]]
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|bgcolor=#e7dcc3|[[Schläfli symbol]]||q{4,3,3,3,3,4}
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|bgcolor=#e7dcc3|Coxeter-Dynkin diagram||{{CDD|nodes_10ru|split2|node|3|node|3|node|split1|nodes_10lu}} = {{CDD|node_h1|4|node|3|node|3|node|3|node|3|node|4|node_h1}}
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|bgcolor=#e7dcc3|5-face type||[[6-demicube|h{4,3<sup>4</sup>}]], [[File:6-demicube t0 D6.svg|60px]]<BR>h<sub>4</sub>{4,3<sup>4</sup>}, [[File:6-demicube t04 D6.svg|60px]]<BR>{3,3}×{3,3} duoprism
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|bgcolor=#e7dcc3|[[Vertex figure]]||
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|bgcolor=#e7dcc3|[[Coxeter group]]||<math>{\tilde{D}}_6</math>×2 = 3<sup>1,1</sup>,3,3,3<sup>1,1</sup>
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|bgcolor=#e7dcc3|Dual||
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|bgcolor=#e7dcc3|Properties||vertex-transitive
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In [[Six-dimensional space|six-dimensional]] [[Euclidean geometry]], the '''quarter 6-cubic honeycomb''' is a uniform space-filling [[Tessellation|tessellation]] (or [[Honeycomb (geometry)|honeycomb]]). It has half the vertices of the [[6-demicubic honeycomb|6-demicubic honeycomb]], and a quarter of the vertices of a 6-cube honeycomb.<ref>Coxeter, '''Regular and Semi-Regular Polytopes III''', (1988), p318</ref> Its facets are [[6-demicube|6-demicube]]s, stericated 6-demicubes, and {3,3}×{3,3} [[Duoprism|duoprism]]s.

== Related honeycombs ==

== See also ==
Regular and uniform honeycombs in 5-space:
*6-cube honeycomb
*6-demicube honeycomb
* [[6-simplex honeycomb|6-simplex honeycomb]]
* Truncated 6-simplex honeycomb
* [[Omnitruncated 6-simplex honeycomb]]

== Notes ==
{{reflist}}

== References ==
* '''Kaleidoscopes: Selected Writings of [[Biography:Harold Scott MacDonald Coxeter|H. S. M. Coxeter]]''', edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, {{isbn|978-0-471-01003-6}} [http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html]
** (Paper 24) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes III'', [Math. Zeit. 200 (1988) 3-45] See p318 [https://books.google.com/books?id=fUm5Mwfx8rAC&dq=%22quarter+cubic+honeycomb%22+q%7B4%2C3%2C4%7D&pg=PA318]
* {{KlitzingPolytopes|flat.htm|6D|Euclidean tesselations#6D}}

{{Honeycombs}}

[[Category:Honeycombs (geometry)]]
[[Category:7-polytopes]]

{{Sourceattribution|Quarter 6-cubic honeycomb}}