Cyclotruncated 6-simplex honeycomb
| Cyclotruncated 6-simplex honeycomb | |
|---|---|
| (No image) | |
| Type | Uniform honeycomb |
| Family | Cyclotruncated simplectic honeycomb |
| Schläfli symbol | t0,1{3[7]} |
| Coxeter diagram | File:CDel branch 11.pngFile:CDel 3ab.pngFile:CDel nodes.pngFile:CDel 3ab.pngFile:CDel nodes.pngFile:CDel split2.png
|
| 6-face types | {35} File:6-simplex t0.svg t{35} File:6-simplex t01.svg 2t{35} File:6-simplex t12.svg 3t{35} File:6-simplex t23.svg |
| Vertex figure | Elongated 5-simplex antiprism |
| Symmetry | ×2, [[3[7]]] |
| 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
Template:6-simplex honeycomb family
See also
Regular and uniform honeycombs in 6-space:
- 6-cubic honeycomb
- 6-demicubic honeycomb
- 6-simplex honeycomb
- Omnitruncated 6-simplex honeycomb
- 222 honeycomb
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]
This article "Cyclotruncated 6-simplex honeycomb" is from Wikipedia. The list of its authors can be seen in its historical and/or the page Edithistory:Cyclotruncated 6-simplex honeycomb. Articles copied from Draft Namespace on Wikipedia could be seen on the Draft Namespace of Wikipedia and not main one.
