Petrial square tiling

Petrial square tiling
Rank	3
Type	Regular
Space	Euclidean
Notation
Schläfli symbol	$\{4,4\}^\pi$ $\{\infty,4\}_4$
Elements
Faces	$N$ zigzags
Edges	$N\times 2M$
Vertices	$N\times M$
Vertex figure	Square, edge length √2
Related polytopes
Army	Squat
Regiment	Squat
Petrie dual	Square tiling
Abstract properties
Flag count	$N\times 8M$
Schläfli type	{∞,4}
Topological properties
Orientable	Yes
Genus	∞
Properties
Symmetry	R3
Convex	No

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