Prismatorhombated cubic honeycomb

The prismatorhombated cubic honeycomb, or prich, also known as the runcitruncated cubic honeycomb, is a convex uniform honeycomb. 1 small rhombicuboctahedron, 1 truncated cube, 1 cube, and 2 octagonal prisms join at each vertex of this honeycomb. As the name suggests, it is the runcitruncation of the cubic honeycomb.

This honeycomb can be subsymmetrically faceted into a runcicantic snub cubic honeycomb, although it cannot be made scaliform.

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


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

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