Petrial hexagonal tiling

Petrial hexagonal tiling
Rank	3
Dimension	2
Type	Regular
Space	Euclidean
Notation
Schläfli symbol	{6,3}π {∞,3}6
Elements
Faces	$N$ zigzags
Edges	$N\times 3M$
Vertices	$N\times 2M$
Vertex figure	Triangle, edge length √3
Related polytopes
Army	Hexat
Regiment	Hexat
Petrie dual	Hexagonal tiling
Abstract & topological properties
Flag count	$N\times 12M$
Schläfli type	{∞,3}
Orientable	Yes
Genus	∞
Properties
Convex	No
Dimension vector	(0,1,1)

The petrial hexagonal tiling is one of the three regular skew tilings of the Euclidean plane. 3 zigzags meet at each vertex. The petrial hexagonal tiling is the Petrie dual of the hexagonal tiling.

Vertex coordinates

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

Related polytopes

The Petrial hexagonal tiling as the apeir of the triangle

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

The rectification of the petrial hexagonal tiling is the triangular-hemiapeirogonal tiling, which is a uniform tiling.