Truncated square prismatic honeycomb

The truncated square prismatic honeycomb, or tassiph, is a convex uniform honeycomb. 2 cubes and 4 octagonal prisms join at each vertex of this honeycomb. As the name suggests, it is the honeycomb product of the truncated square tiling and the apeirogon.

Vertex coordinates
Coordinates for the vertices of a truncated square prismatic honeycomb of edge length 1 are given by all permutations of where i, j, and k range over the integers.
 * $$\left(±\frac12+(1+\sqrt2)i,\,±\frac{1+\sqrt2}{2}+j(1+\sqrt2),\,k\right),$$

Representations
A truncated square prismatic honeycomb has the following Coxeter diagrams:


 * x∞o x4x4o
 * x∞x x4x4o
 * x∞o x4x4x
 * x∞x x4x4x