View source for Quarter 8-cubic honeycomb

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!bgcolor=#e7dcc3 colspan=2|quarter 8-cubic honeycomb
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|bgcolor=#ffffff align=center colspan=2|(No image)
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|bgcolor=#e7dcc3|Type||[[Uniform_9-polytope#Regular_and_uniform_honeycombs|Uniform 8-honeycomb]]
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|bgcolor=#e7dcc3|Family||[[Quarter hypercubic honeycomb]]
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|bgcolor=#e7dcc3|[[Schläfli symbol]]||q{4,3,3,3,3,3,3,4}
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|bgcolor=#e7dcc3|[[Coxeter diagram]]||{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node|3|node|split1|nodes_10lu}} = {{CDD|node_h1|4|node|3|node|3|node|3|node|3|node|3|node|3|node|4|node_h1}}
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|bgcolor=#e7dcc3|7-face type||[[8-demicube|h{4,3<sup>6</sup>}]], [[File:8-demicube t0 D8.svg|60px]]<BR>[[Pentic 8-cube|h<sub>6</sub>{4,3<sup>6</sup>}]], [[File:8-demicube t06 D8.svg|60px]]<BR>{3,3}×{3<sup>2,1,1</sup>} duoprism<BR>{3<sup>1,1,1</sup>}×{3<sup>1,1,1</sup>} duoprism
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|bgcolor=#e7dcc3|[[Vertex figure]]||
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|bgcolor=#e7dcc3|[[Coxeter group]]||<math>{\tilde{D}}_8</math>×2 = [[3<sup>1,1</sup>,3,3,3,3,3<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 [[Eight-dimensional space|seven-dimensional]] [[Euclidean geometry]], the '''quarter 8-cubic honeycomb''' is a uniform space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]). It has half the vertices of the [[8-demicubic honeycomb]], and a quarter of the vertices of a [[8-cube honeycomb]].<ref>Coxeter, '''Regular and Semi-Regular Polytopes III''', (1988), p318</ref> Its facets are [[8-demicube]]s h{4,3<sup>6</sup>}, [[pentic 8-cube]]s h<sub>6</sub>{4,3<sup>6</sup>}, {3,3}×{3<sup>2,1,1</sup>} and {3<sup>1,1,1</sup>}×{3<sup>1,1,1</sup>} [[duoprism]]s.
  
== See also ==
Regular and uniform honeycombs in 8-space:
*[[8-cube honeycomb]]
*[[8-demicube honeycomb]]
*[[8-simplex honeycomb]]
*[[Truncated 8-simplex honeycomb]]
*[[Omnitruncated 8-simplex honeycomb]]

== Notes ==
{{reflist}}

== References ==
* '''Kaleidoscopes: Selected Writings of [[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|7D|Euclidean tesselations#7D}}
{{Honeycombs}}

[[Category:Honeycombs (geometry)]]
[[Category:9-polytopes]]