Truncated cubic honeycomb

The truncated cubic honeycomb, or tich, is a convex uniform honeycomb. 1 octahedron and 4 truncated cubes join at each vertex of this honeycomb. As the name suggests, it is the truncation of the cubic honeycomb.

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


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

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

Representations
A truncated cubic honeycomb has the following Coxeter diagrams:


 * x4x3o4o (regular)
 * o3x3o *b4x (S4 symmetry)
 * wx4xo3ox4xw&#zx