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.

This honeycomb can be alternated into a snub square antiprismatic honeycomb, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create an edge-snub square prismatic honeycomb, which is also nonuniform.

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: