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.
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* 6 lattice
The A*
6 lattice (also called A7
6) 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.
∪ ∪ ∪ ∪ ∪ ∪ = dual of
Related polytopes and honeycombs
This honeycomb is one of 17 unique uniform honeycombs constructed by the
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: