Elongated triangular tiling

The elongated triangular tiling, or etrat, is one of the eleven convex uniform tilings of the Euclidean plane. 3 triangles and 2 squares join at each vertex of this tiling.

It is the only one of the 11 regular and uniform convex tilings of the plane to not be derivable from the regulars by truncation operations or alternation. It can be thought of as being constructed from the triangular tiling with layers of squares being inserted between adjacent layers of triangles. It can also be considered a blend of infinitely many apeirogonal antiprisms and apeirogonal prisms.

Vertex coordinates
The vertices of an elongated triangular tiling of edge length 1 are given by

where i and j range over the integers.
 * $$\left(i\frac{2+\sqrt3}{2}\pm\frac12,\,j+\frac{i}{2}\right),$$