Petrial blended triangular tiling

Petrial blended triangular tiling
Rank	3
Type	Regular
Notation
Schläfli symbol	$\{\infty,6\}_3\#\{\}$ $\{3,6\}^\pi\#\{\}$ $\{6,6\mid *2\}^\pi$
Elements
Faces	N zigzags
Edges	N×3M
Vertices	N×M
Vertex figure	Hexagon
Petrie polygons	Skew triangles
Related polytopes
Army	Hexagonal tiling prism
Regiment	Blended triangular tiling
Petrie dual	Blended triangular tiling
Abstract & topological properties
Schläfli type	{∞,6}
Properties
Symmetry	V3×A1
Convex	No

The petrial blended triangular tiling is a regular skew apeirohedron. It can be constructed as the blend of the petrial triangular tiling with a digon or as the petrial of the blended triangular tiling.

Vertex coordinates

The vertex coordinates of a petrial blended triangular tiling are the same as those of the blended triangular tiling. With edge length 1 and height h, the verteix coordinates are given by

• $\left(\frac{Hi\sqrt{3}}{2},Hj+\frac{Hi}{2},\pm\frac{h}{2}\right)$

where i and j range over the integers, and H is $\sqrt{1-h^2}$ (Note that $0<h<1$ must always be true for H to be a real number and for the blend to be non-degenerate).

References

• jan Misali (2020). "there are 48 regular polyhedra"
• McMullen, Peter; Schulte, Egon (1997). "Regular Polytopes in Ordinary Space". Discrete Computational Geometry. 17: 449–478.