It is the first tessellation in the demihypercube honeycomb family which, with all the next ones, is not regular, being composed of two different types of uniform facets.
The vertex arrangement of the 5-demicubic honeycomb is the D5 lattice which is the densest known sphere packing in 5 dimensions.
[1] The 40 vertices of the rectified 5-orthoplex vertex figure of the 5-demicubic honeycomb reflect the kissing number 40 of this lattice.
Each symmetry can be represented by arrangements of different colors on the 32 5-demicube facets around each vertex.
The 20 permutations are listed with its highest extended symmetry relation: , , , Regular and uniform honeycombs in 5-space: