Each vertex is shared by 12 5-simplexes, 30 rectified 5-simplexes, and 20 birectified 5-simplexes.
These facet types occur in proportions of 2:2:1 respectively in the whole honeycomb.
The 30 vertices of the stericated 5-simplex vertex figure represent the 30 roots of the
Coxeter group allows for automorphisms that map diagram nodes (mirrors) on to each other.
So the various 12 honeycombs represent higher symmetries based on the ring arrangement symmetry in the diagrams: The 5-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 5-space: