# Petrial triangular tiling

Petrial triangular tiling
Rank3
TypeRegular
SpaceEuclidean
Notation
Schläfli symbol${\displaystyle \{3,6\}^\pi}$
${\displaystyle \{\infty,6\}_3}$
Elements
Faces${\displaystyle N}$ zigzags
Edges${\displaystyle N\times 3M}$
Vertices${\displaystyle N\times M}$
Vertex figureHexagon, edge length 1
Related polytopes
ArmyTrat
RegimentTrat
Petrie dualTriangular tiling
Abstract properties
Flag count${\displaystyle N\times 12M}$
Schläfli type{∞,6}
Topological properties
OrientableNo
Genus
Properties
ConvexNo

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

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

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.