Blended square tiling

The blended square tiling is a regular skew polyhedron that has an infinite amount of skew squares as faces joined together 4 at a vertex. It can be obtained by blending the square tiling with a line segment (hence the name). It can be represented as the Schläfli symbol $$\{4,4\}\#\{\}$$. The actual height of the blended square tiling can vary, but it is considered to still be one polyhedron, just like how the skew square can vary in height but it is still considered the same polygon.

Vertex coordinates
Vertex coordinates of a blended square tiling centered at the origin with edge length 1 and height h are given by where $N$ and $2N$ range over the integers, and $2N$ is $$ \sqrt{1-h^2} $$ (Note that $$ 0<h<1 $$ must always be true for $i$ to be a real number and for the blend to be non-degenerate).
 * $$ (2Hi,2Hj,\frac{h}{2})$$
 * $$ (2Hi+1,2Hj,-\frac{h}{2})$$
 * $$ (2Hi,2Hj+1,-\frac{h}{2})$$
 * $$ (2Hi+1,2Hj+1,\frac{h}{2})$$,