View source for Quarter 5-cubic honeycomb

{| class="wikitable" align="right" style="margin-left:10px" width="360"
!bgcolor=#e7dcc3 colspan=2|Bitruncated tesseractic honeycomb
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|bgcolor=#ffffff align=center colspan=2|(No image)
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|bgcolor=#e7dcc3|Type||[[Uniform_polyteron#Regular_and_uniform_honeycombs|Uniform 4-honeycomb]]
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|bgcolor=#e7dcc3|[[Schläfli symbol]]||t<sub>12</sub>{4,3,3,4}<BR>t<sub>12</sub>{4,3<sup>1,1</sup>}<BR>t<sub>23</sub>{4,3<sup>1,1</sup>}<BR>q<sub>2</sub>{4,3,3,3,4}
|-
|bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram]]||
{{CDD|node|4|node_1|3|node_1|3|node|4|node}}<BR>
{{CDD|node|4|node_1|3|node_1|split1|nodes}}<BR>
{{CDD|nodes_11|split2|node_1|3|node|4|node}}<BR>
{{CDD|nodes_10ru|split2|node_1|split1|nodes_10lu}} = {{CDD|node_1|split1|nodes|4a4b|nodes_h1h1}}
|-
|bgcolor=#e7dcc3|4-face type||[[Bitruncated tesseract]] [[File:Schlegel half-solid bitruncated 16-cell.png|40px]]<BR>[[Truncated 16-cell]] [[File:Schlegel half-solid truncated 16-cell.png|40px]]
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|bgcolor=#e7dcc3|Cell type||[[Octahedron]] [[File:Octahedron.png|20px]]<BR>[[Truncated tetrahedron]] [[File:Truncated tetrahedron.png|20px]]<BR>[[Truncated octahedron]] [[File:Truncated octahedron.png|20px]]
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|bgcolor=#e7dcc3|Face type||{3}, {4}, {6}
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|bgcolor=#e7dcc3|[[Vertex figure]]||square [[duopyramid]]
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|bgcolor=#e7dcc3|[[Coxeter group]]||<math>{\tilde{C}}_4</math> = [4,3,3,4]<BR><math>{\tilde{B}}_4</math> = [4,3<sup>1,1</sup>]<BR><math>{\tilde{D}}_4</math> = [3<sup>1,1,1,1</sup>]
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|bgcolor=#e7dcc3|Dual||
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|bgcolor=#e7dcc3|Properties||[[vertex-transitive]]
|}
In [[Four-dimensional space|four-dimensional]] [[Euclidean geometry]], the '''bitruncated tesseractic honeycomb''' is a uniform  space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]) in Euclidean 4-space. It is constructed by a [[bitruncation]] of a [[tesseractic honeycomb]]. It is also called a '''cantic quarter tesseractic honeycomb''' from its q<sub>2</sub>{4,3,3,4} construction.

== Other names==
* Bitruncated tesseractic tetracomb (batitit)

== Related honeycombs==
{{C4_honeycombs}}

{{B4_honeycombs}}

{{D4_honeycombs}}

== See also ==
Regular and uniform honeycombs in 4-space:
*[[Tesseractic honeycomb]]
*[[Demitesseractic honeycomb]]
*[[24-cell honeycomb]]
*[[Truncated 24-cell honeycomb]]
*[[Snub 24-cell honeycomb]]
* [[5-cell honeycomb]]
* [[Truncated 5-cell honeycomb]]
* [[Omnitruncated 5-cell honeycomb]]

==Notes==
{{reflist}}

== References ==
* '''Kaleidoscopes: Selected Writings of 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 [http://books.google.com/books?id=fUm5Mwfx8rAC&lpg=PA318&ots=dnT1LYgmij&dq=%22quarter%20cubic%20honeycomb%22%20q%7B4%2C3%2C4%7D&pg=PA318#v=onepage&q=%22quarter%20cubic%20honeycomb%22%20q%7B4,3,4%7D&f=false]
* [[George Olshevsky]], ''Uniform Panoploid Tetracombs'', Manuscript (2006) ''(Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)''
* {{KlitzingPolytopes|flat.htm|4D|Euclidean tesselations#4D}} x3x3x *b3o *b3o , x3x3x *b3o4o , o3x3o *b3x4o , o4x3x3o4o - batitit - O92
* {{cite book |author=Conway JH, Sloane NJH |year=1998 |title=Sphere Packings, Lattices and Groups |edition=3rd |isbn=0-387-98585-9}}
{{Honeycombs}}

[[Category:Honeycombs (geometry)]]
[[Category:5-polytopes]]