Small rhombated cubic honeycomb

The small rhombated cubic honeycomb, or srich, also known as the cantellated cubic honeycomb, is a convex uniform honeycomb. 1 cuboctahedron, 2 small rhombicuboctahedra, and 2 cubes join at each vertex of this honeycomb. As the name suggests, it is the cantellation of the cubic honeycomb.

Vertex coordinates
The vertices of a small rhombated cubic honeycomb of edge length 1 are given by all permutations of:


 * $$\left(±\frac12+(1+\sqrt2)i,\,±\frac12+(1+\sqrt2)j,\,±\frac{1+\sqrt2}{2}+(1+\sqrt2)k\right),$$

Where i, j, and k range over the integers.

Representations
A small rhombated cubic honeycomb has the following Coxeter diagrams:


 * x4o3x4o (regular)
 * x3o3x *b4x (S4 symmetry)
 * s4x3o4x (as alternated faceting)