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Omnitruncated 8 simplex honeycomb

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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.

Contents

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* 8 lattice

The A*
8
lattice (also called A9
8
) 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

= dual of .

This honeycomb is one of 45 unique uniform honeycombs constructed by the A ~ 8 Coxeter group. The symmetry can be multiplied by the ring symmetry of the Coxeter diagrams:

References

Omnitruncated 8-simplex honeycomb Wikipedia