- Source: Omnitruncated 6-simplex honeycomb
- Daftar bentuk matematika
- Omnitruncated 6-simplex honeycomb
- 6-simplex honeycomb
- Omnitruncated 5-simplex honeycomb
- Omnitruncated 7-simplex honeycomb
- Omnitruncated 8-simplex honeycomb
- Cyclotruncated 6-simplex honeycomb
- Omnitruncated simplicial honeycomb
- Order-6 cubic honeycomb
- Hexagonal tiling
- Bitruncated cubic honeycomb
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).
A*6 lattice
The A*6 lattice (also called A76) 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.
∪
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= dual of
Related polytopes and honeycombs
This honeycomb is one of 17 unique uniform honeycombs constructed by
the
A
~
6
{\displaystyle {\tilde {A}}_{6}}
Coxeter group, grouped by their extended symmetry of the Coxeter–Dynkin diagrams:
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
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]