Square-hemiapeirogonal prismatic honeycomb

The square-hemiapeirogonal prismatic honeycomb is a uniform honeycomb or tesselation of 3D Euclidean space. 4 cubes and 2 square tilings join at each vertex of this honeycomb. It has the vertices and edges of the cubic honeycomb and a subset of its faces.

It is the comb product of a square-hemiapeirogonal tiling and an apeirogon, with the resulting apeirogonal prisms blending into square tilings.

Vertex coordinates
The vertices are the same as those of the cubic honeycomb, given by


 * $$(i,j,k)$$ in which $$i,j,k\in\mathbb{Z}$$.