cyclotruncated 5-simplex honeycomb
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!bgcolor=#e7dcc3 colspan=2|Cyclotruncated 5-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[6]} |
| bgcolor=#e7dcc3|Coxeter diagram | {{CDD|node|split1|nodes_10lur|3ab|nodes_10lru|split2|node}} or {{CDD|branch_11|3ab|nodes|3ab|branch}} |
| bgcolor=#e7dcc3|5-face types | {3,3,3,3} 40px t{3,3,3,3} 40px 2t{3,3,3,3} 40px |
| bgcolor=#e7dcc3|4-face types | {3,3,3} 40px t{3,3,3} 40px |
| bgcolor=#e7dcc3|Cell types | {3,3} 40px t{3,3} 40px |
| bgcolor=#e7dcc3|Face types | {3} 40px t{3} 40px |
| bgcolor=#e7dcc3|Vertex figure | 120px Elongated 5-cell antiprism |
| bgcolor=#e7dcc3|Coxeter groups | ×22, {{Brackets|3{{Bracket|6}}}} |
| bgcolor=#e7dcc3|Properties | vertex-transitive |
In five-dimensional Euclidean geometry, the cyclotruncated 5-simplex honeycomb or cyclotruncated hexateric honeycomb is a space-filling tessellation (or honeycomb). It is composed of 5-simplex, truncated 5-simplex, and bitruncated 5-simplex facets in a ratio of 1:1:1.
Structure
Its vertex figure is an elongated 5-cell antiprism, two parallel 5-cells in dual configurations, connected by 10 tetrahedral pyramids (elongated 5-cells) from the cell of one side to a point on the other. The vertex figure has 8 vertices and 12 5-cells.
It can be constructed as six sets of parallel hyperplanes that divide space. The hyperplane intersections generate cyclotruncated 5-cell honeycomb divisions on each hyperplane.
Related polytopes and honeycombs
{{5-simplex honeycomb family}}
See also
Regular and uniform honeycombs in 5-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}}