Petrial triangular tiling

Petrial triangular tiling
Rank	3
Dimension	2
Type	Regular
Space	Euclidean
Notation
Schläfli symbol	{3,6}π {∞,6}3
Elements
Faces	$N$ zigzags
Edges	$N\times 3M$
Vertices	$N\times M$
Vertex figure	Hexagon, edge length 1
Petrie polygons	$2N\times M$ triangles
Related polytopes
Army	Trat
Regiment	Trat
Petrie dual	Triangular tiling
Abstract & topological properties
Flag count	$N\times 12M$
Schläfli type	{∞,6}
Orientable	No
Genus	∞
Properties
Symmetry	V3
Convex	No

The Petrial triangular tiling is one of three regular skew tilings of the Euclidean plane. Six zigzags meet at a vertex and it is the Petrie dual of the triangular tiling.

Vertex coordinates

The vertex coordinates of a Petrial triangular tiling with edge length one are the same as those of the triangular tiling.

Related polytopes

The Petrial triangular tiling as the apeir of the hexagon

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

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