Petrial square tiling

Petrial square tiling
Rank	3
Dimension	2
Type	Regular
Space	Euclidean
Notation
Schläfli symbol	{4,4}π {∞,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
Skewing	Petrial square tiling
Abstract & topological properties
Flag count	$N\times 8M$
Schläfli type	{∞,4}
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

The vertex coordinates of the Petrial square tiling are the same as those of the square tiling.

Related polytopes

The Petrial square tiling as the apeir of the square

The Petrial square tiling is the apeir of the square, its vertex figure.

The rectification of the Petrial square tiling is the square-hemiapeirogonal tiling, which is a uniform tiling.