Square tiling prism

The square tiling prism or cubic slab honeycomb is a prismatic uniform honeycomb of the Euclidean plane. It consists of 2 square tilings and ∞ cubes. Each vertex joins one apeirogon and two squares. It is a prism based on the square tiling.

Vertex coordinates
A square tiling prism of edge length 1 has vertex coordinates given by, where $$i,\,j$$ range over the integers:
 * $$\left(±\tfrac12,\,i,\,j,\,0\right)$$

Semi-uniform variant
The apeirogonal prism has a semi-uniform variant of the form x y4o4o that maintains its full symmetry. This variant uses square prisms as its sides.