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).
The A*8 lattice (also called A98) 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 .
Regular and uniform honeycombs in 8-space: