Cyclotruncated 8-simplex honeycomb
| Cyclotruncated 8-simplex honeycomb | |
|---|---|
| (No image) | |
| Type | Uniform honeycomb |
| Family | Cyclotruncated simplectic honeycomb |
| Schläfli symbol | t0,1{3[9]} |
| Coxeter diagram |     
|
| 8-face types | {37}  , t0,1{37}  t1,2{37}  , t2,3{37} File:8-simplex t23.svgt3,4{37} File:8-simplex t34.svg |
| Vertex figure | Elongated 7-simplex antiprism |
| Symmetry | ×2, [[3[9]]] |
| Properties | vertex-transitive |
In eight-dimensional Euclidean geometry, the cyclotruncated 8-simplex honeycomb is a space-filling tessellation (or honeycomb). The tessellation fills space by 8-simplex, truncated 8-simplex, bitruncated 8-simplex, tritruncated 8-simplex, and quadritruncated 8-simplex facets. These facet types occur in proportions of 2:2:2:2:1 respectively in the whole honeycomb.
Structure
It can be constructed by nine sets of parallel hyperplanes that divide space. The hyperplane intersections generate cyclotruncated 7-simplex honeycomb divisions on each hyperplane.
Related polytopes and honeycombs
Template:8-simplex honeycomb family
See also
Regular and uniform honeycombs in 8-space:
- 8-cubic honeycomb
- 8-demicubic honeycomb
- 8-simplex honeycomb
- Omnitruncated 8-simplex honeycomb
- 521 honeycomb
- 251 honeycomb
- 152 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]
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