Cyclotruncated 5-simplex honeycomb
| Cyclotruncated 5-simplex honeycomb | |
|---|---|
| (No image) | |
| Type | Uniform honeycomb |
| Family | Cyclotruncated simplectic honeycomb |
| Schläfli symbol | t0,1{3[6]} |
| Coxeter diagram |  File:CDel split1.pngFile:CDel nodes 10lur.pngFile:CDel 3ab.pngFile:CDel nodes 10lru.pngFile:CDel split2.png or File:CDel branch 11.pngFile:CDel 3ab.pngFile:CDel nodes.pngFile:CDel 3ab.pngFile:CDel branch.png
|
| 5-face types | {3,3,3,3} File:5-simplex t0.svg t{3,3,3,3} File:5-simplex t01.svg 2t{3,3,3,3} File:5-simplex t12.svg |
| 4-face types | {3,3,3} File:4-simplex t0.svg t{3,3,3} File:4-simplex t01.svg |
| Cell types | {3,3} File:3-simplex t0.svg t{3,3} File:3-simplex t01.svg |
| Face types | {3} File:2-simplex t0.svg t{3} File:2-simplex t01.svg |
| Vertex figure |  Elongated 5-cell antiprism |
| Coxeter groups | ×22, [[3[6]]] |
| 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
Template:5-simplex honeycomb family
See also
Regular and uniform honeycombs in 5-space:
Notes
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 Search this book on
. [1]
- (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]
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