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).

A lattice

The A lattice (also called A) 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 In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators). For each seed t ...

of this lattice is an omnitruncated 8-simplex : ∪ ∪ ∪ ∪ ∪ ∪ ∪ ∪ = dual of .

Related polytopes and honeycombs

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,

** (Paper 22) H.S.M. Coxeter, ''Regular and Semi Regular Polytopes I'', ath. 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'', ath. Zeit. 200 (1988) 3-45{{Honeycombs Honeycombs (geometry) 9-polytopes

A lattice

Related polytopes and honeycombs

See also

Notes

References