This
vertex arrangement is called the A6 lattice or
6-simplex lattice. The 42 vertices of the
expanded 6-simplex vertex figure represent the 42 roots of the {\tilde{A}}_6
Coxeter group. It is the 6-dimensional case of a
simplectic honeycomb. Around each vertex figure are 126 facets: 7+7
6-simplex, 21+21
rectified 6-simplex, 35+35
birectified 6-simplex, with the count distribution from the 8th row of
Pascal's triangle. The A lattice (also called A) 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 ==