Cyclotruncated 6-simplex honeycomb
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!bgcolor=#e7dcc3 colspan=2|Cyclotruncated 6-simplex honeycomb | |
| bgcolor=#ffffff align=center colspan=2|(No image) | |
| bgcolor=#e7dcc3|Type | Uniform honeycomb |
| bgcolor=#e7dcc3|Family | Cyclotruncated simplectic honeycomb |
| bgcolor=#e7dcc3|Schläfli symbol | t0,1{3[7]} |
| bgcolor=#e7dcc3|Coxeter diagram | {{CDD|branch_11|3ab|nodes|3ab|nodes|split2|node}} |
| bgcolor=#e7dcc3|6-face types | {35} 30px t{35} 30px 2t{35} 30px 3t{35} 30px |
| bgcolor=#e7dcc3|Vertex figure | Elongated 5-simplex antiprism |
| bgcolor=#e7dcc3|Symmetry | ×2, {{Brackets|3{{Bracket|7}}}} |
| bgcolor=#e7dcc3|Properties | vertex-transitive |
In six-dimensional Euclidean geometry, the cyclotruncated 6-simplex honeycomb is a space-filling tessellation (or honeycomb). The tessellation fills space by 6-simplex, truncated 6-simplex, bitruncated 6-simplex, and tritruncated 6-simplex facets. These facet types occur in proportions of 2:2:2:1 respectively in the whole honeycomb.
Structure
It can be constructed by seven sets of parallel hyperplanes that divide space. The hyperplane intersections generate cyclotruncated 5-simplex honeycomb divisions on each hyperplane.
Related polytopes and honeycombs
{{6-simplex honeycomb family}}
See also
Regular and uniform honeycombs in 6-space:
Notes
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References
- 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}}