The tessellation fills space by 7-simplex, rectified 7-simplex, birectified 7-simplex, and trirectified 7-simplex facets.
These facet types occur in proportions of 2:2:2:1 respectively in the whole honeycomb.
The 56 vertices of the expanded 7-simplex vertex figure represent the 56 roots of the
[1] It is the 7-dimensional case of a simplectic honeycomb.
Around each vertex figure are 254 facets: 8+8 7-simplex, 28+28 rectified 7-simplex, 56+56 birectified 7-simplex, 70 trirectified 7-simplex, with the count distribution from the 9th row of Pascal's triangle.
The A*7 lattice (also called A87) is the union of eight A7 lattices, and has the vertex arrangement to the dual honeycomb of the omnitruncated 7-simplex honeycomb, and therefore the Voronoi cell of this lattice is an omnitruncated 7-simplex.
Coxeter group, grouped by their extended symmetry of rings within the regular octagon diagram:
The 7-simplex honeycomb can be projected into the 4-dimensional tesseractic honeycomb by a geometric folding operation that maps two pairs of mirrors into each other, sharing the same vertex arrangement: Regular and uniform honeycombs in 7-space: