Petrial triangular tiling

Petrial triangular tiling
Rank	3
Type	Regular
Space	Euclidean
Notation
Schläfli symbol	$\{3,6\}^\pi$ $\{\infty,6\}_3$
Elements
Faces	$N$ zigzags
Edges	$N\times 3M$
Vertices	$N\times M$
Vertex figure	Hexagon, edge length 1
Related polytopes
Army	Trat
Regiment	Trat
Petrie dual	Triangular tiling
Abstract properties
Flag count	$N\times 12M$
Schläfli type	{∞,6}
Topological properties
Orientable	No
Genus	∞
Properties
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 the triangular tiling, being

• $(i\frac{\sqrt{3}}{2} , j+\frac{i}{2})$,

where i and j range over the integers.

Related polyhedra

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