Black's approximation
| Omnitruncated 6-simplex honeycomb | |
|---|---|
| (No image) | |
| Type | Uniform honeycomb |
| Family | Omnitruncated simplectic honeycomb |
| Schläfli symbol | {3[8]} |
| Coxeter–Dynkin diagrams | Template:CDD |
| Facets |  t0,1,2,3,4,5{3,3,3,3,3} |
| Vertex figure |  Irr. 6-simplex |
| Symmetry | ×14, [7[3[7]]] |
| Properties | vertex-transitive |
In six-dimensional Euclidean geometry, the omnitruncated 6-simplex honeycomb is a space-filling tessellation (or honeycomb). It is composed entirely of omnitruncated 6-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 seven A6 lattices, and has the vertex arrangement of the dual to the omnitruncated 6-simplex honeycomb, and therefore the Voronoi cell of this lattice is the omnitruncated 6-simplex.
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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Projection by folding
The omnitruncated 6-simplex honeycomb can be projected into the 4-dimensional cubic honeycomb by a geometric folding operation that maps two pairs of mirrors into each other, sharing the same vertex arrangement:
| Template:CDD | |
| Template:CDD |
See also
Regular and uniform honeycombs in 6-space:
- 6-cubic honeycomb
- 6-demicubic honeycomb
- 6-simplex honeycomb
- Truncated 6-simplex honeycomb
- 222 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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