# Petrial hexagonal tiling

Petrial hexagonal tiling Rank3
TypeRegular
SpaceEuclidean
Notation
Schläfli symbol$\{6,3\}^\pi$ $\{\infty,3\}_6$ Elements
Faces$N$ zigzags
Edges$N\times 3M$ Vertices$N\times 2M$ Vertex figureTriangle, edge length 3
Related polytopes
ArmyHexat
RegimentHexat
Petrie dualHexagonal tiling
Abstract properties
Flag count$N\times 12M$ Schläfli type{∞,3}
Topological properties
OrientableYes
Genus
Properties
ConvexNo

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

Coordinates for the vertices of a petrial hexagonal tiling of edge length 1 are given by

• $\left(3i\pm\frac12,\,\sqrt3j+\frac{\sqrt3}{2}\right)$ ,
• $\left(3i\pm1,\,\sqrt3j\right)$ ,

where i and j range over the integers.

## Related polyhedra

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