View source for Cyclotruncated 7-simplex honeycomb

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!bgcolor=#e7dcc3 colspan=2|Cyclotruncated 7-simplex honeycomb
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|bgcolor=#ffffff align=center colspan=2|(No image)
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|bgcolor=#e7dcc3|Type||Uniform honeycomb
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|bgcolor=#e7dcc3|Family||[[Cyclotruncated simplectic honeycomb]]
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|bgcolor=#e7dcc3|[[Schläfli symbol]]||t<sub>0,1</sub>{3<sup>[8]</sup>}
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|bgcolor=#e7dcc3|Coxeter diagram||{{CDD|branch_11|3ab|nodes|3ab|nodes|3ab|branch}}
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|bgcolor=#e7dcc3|7-face types||[[7-simplex|{3<sup>6</sup>}]] [[File:7-simplex t0.svg|30px]]<BR>t<sub>0,1</sub>{3<sup>6</sup>} 30px<BR>t<sub>1,2</sub>{3<sup>6</sup>} 30px<BR>t<sub>2,3</sub>{3<sup>6</sup>} [[File:7-simplex t23.svg|30px]]
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|bgcolor=#e7dcc3|Vertex figure||Elongated 6-simplex antiprism
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|bgcolor=#e7dcc3|Symmetry||<math>{\tilde{A}}_7</math>×2<sub>2</sub>, 3<sup>[8]</sup>
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|bgcolor=#e7dcc3|Properties||vertex-transitive
|}
In seven-dimensional [[Euclidean geometry]], the '''cyclotruncated 7-simplex honeycomb''' is a space-filling [[Tessellation|tessellation]] (or [[Honeycomb (geometry)|honeycomb]]). The tessellation fills space by [[7-simplex|7-simplex]], truncated 7-simplex, bitruncated 7-simplex, and tritruncated 7-simplex facets. These facet types occur in proportions of 1:1:1:1 respectively in the whole honeycomb.
==Structure==
It can be constructed by eight sets of parallel [[Hyperplane|hyperplane]]s that divide space. The hyperplane intersections generate  [[Cyclotruncated 6-simplex honeycomb|cyclotruncated 6-simplex honeycomb]] divisions on each hyperplane.

== Related polytopes and honeycombs ==

{{7-simplex honeycomb family}}

==See also==
Regular and uniform honeycombs in 7-space:
*[[7-cubic honeycomb|7-cubic honeycomb]]
*[[7-demicubic honeycomb|7-demicubic honeycomb]]
*[[7-simplex honeycomb|7-simplex honeycomb]]
*[[Omnitruncated 7-simplex honeycomb]]
*3<sub>31</sub> honeycomb

==Notes==
{{reflist}}

== References ==
* [[Biography:Norman Johnson (mathematician)|Norman Johnson]] ''Uniform Polytopes'', Manuscript (1991)
* '''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 22) H.S.M. Coxeter, ''Regular and Semi Regular Polytopes I'', [Math. Zeit. 46 (1940) 380-407, MR 2,10] (1.9 Uniform space-fillings)
** (Paper 24) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes III'', [Math. Zeit. 200 (1988) 3-45]
{{Honeycombs}}

[[Category:Honeycombs (geometry)]]

{{Sourceattribution|Cyclotruncated 7-simplex honeycomb}}