Truncated square tiling

The truncated square tiling, or tosquat, is one of the eleven convex uniform tilings of the Euclidean plane. 1 square and 2 octagons join at each vertex of this tiling. As its name suggests, it is the truncation of the regular square tiling.

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

Representations
A truncated square tiling has the following Coxeter diagrams:


 * x4x4o (regular)
 * x4x4x (as omnitruncated square tiling)
 * s4o4x (as alternated facting)
 * s4x4x