Omnitruncated 5-simplex honeycomb

In five-dimensional Euclidean geometry, the omnitruncated 5-simplex honeycomb or omnitruncated hexateric honeycomb is a space-filling tessellation (or honeycomb). It is composed entirely of omnitruncated 5-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).

A5* lattice
The A$$ lattice (also called A$$) is the union of six A5 lattices, and is the dual vertex arrangement to the omnitruncated 5-simplex honeycomb, and therefore the Voronoi cell of this lattice is an omnitruncated 5-simplex. ∪ ∪ ∪ ∪ ∪ = dual of

Projection by folding
The omnitruncated 5-simplex honeycomb can be projected into the 3-dimensional omnitruncated cubic honeycomb by a geometric folding operation that maps two pairs of mirrors into each other, sharing the same 3-space vertex arrangement: