Zeta Equulei
| Omnitruncated 8-simplex honeycomb | |
|---|---|
| (No image) | |
| Type | Uniform honeycomb |
| Family | Omnitruncated simplectic honeycomb |
| Schläfli symbol | {3[9]} |
| Coxeter–Dynkin diagrams | Template:CDD |
| 7-face types | t01234567{3,3,3,3,3,3,3} |
| Vertex figure |  Irr. 8-simplex |
| Symmetry | ×18, [9[3[9]]] |
| Properties | vertex-transitive |
In eight-dimensional Euclidean geometry, the omnitruncated 8-simplex honeycomb is a space-filling tessellation (or honeycomb). It is composed entirely of omnitruncated 8-simplex facets.
The facets of all omnitruncated simplectic honeycombs are called permutahedra and can be positioned in n+1 space with integral coordinates, permutations of the whole numbers (0,1,..,n).
ATemplate:Sup sub lattice
The ATemplate:Sup sub lattice (also called ATemplate:Sup sub) is the union of nine A8 lattices, and has the vertex arrangement of the dual honeycomb to the omnitruncated 8-simplex honeycomb, and therefore the Voronoi cell of this lattice is an omnitruncated 8-simplex
Template:CDD + Template:CDD + Template:CDD + Template:CDD + Template:CDD + Template:CDD + Template:CDD + Template:CDD + Template:CDD = dual of Template:CDD.
Related polytopes and honeycombs
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See also
Regular and uniform honeycombs in 8-space:
- 8-cubic honeycomb
- 8-demicubic honeycomb
- 8-simplex honeycomb
- Truncated 8-simplex honeycomb
- 521 honeycomb
- 251 honeycomb
- 152 honeycomb
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 [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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