The tessellation fills space by 6-simplex, rectified 6-simplex, and birectified 6-simplex facets.
These facet types occur in proportions of 1:1:1 respectively in the whole honeycomb.
The 42 vertices of the expanded 6-simplex vertex figure represent the 42 roots of the
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.
3 The 6-simplex honeycomb can be projected into the 3-dimensional cubic 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 6-space: