Great prismated cubic honeycomb

The great prismated cubic honeycomb, or gippich, also known as the omnitruncated cubic honeycomb, or otch, is a convex uniform honeycomb. 2 great rhombicuboctahedra and 2 octagonal prisms join at each vertex of this honeycomb. As the name suggests, it is the omnitruncate of the R4 family.

This honeycomb can be alternated into a snub bicubic honeycomb, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create an edge-snub cubic honeycomb, cantic bisnub cubic honeycomb or great birhombitetrahedral honeycomb, which are nonuniform.

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


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

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