Petrial square tiling

The petrial square tiling is one of the three regular skew tilings of the Euclidean plane. 4 skew apeirogons meet at each vertex. The petrial square tiling is the Petrie dual of the square tiling, so it is in the squat regiment.

Vertex coordinates
Coordinates for the vertices of a petrial square tiling of edge length 1 are given by


 * $$(i,j) ,$$

where i and j range over the integers.

Related polyhedra
The rectification of the petrial square tiling is the square-hemiapeirogonal tiling, which is a uniform tiling.