Petrial mucube

Petrial mucube
Rank	3
Notation
Schläfli symbol	$\{4,6\mid 4\}^\pi$ $\{\infty,6\}_{4,4}$
Elements
Faces	N triangular helices
Edges	3M×N
Vertices	M×N
Vertex figure	Skew hexagon
Petrie polygons	squares
Related polytopes
Army	Cubic honeycomb
Regiment	Cubic honeycomb
Petrie dual	Mucube
Abstract properties
Flag count	12M×N
Schläfli type	{∞,6}
Topological properties
Orientable	Yes
Properties
Convex	No

A section of the mucube with a Petrie polygon highlighted in red.

The Petrial mucube is a regular skew apeirohedron in 3 dimensional Euclidean space. It is the Petrie dual of the mucube.

Vertex coordinates

It's vertex coordinates are the same as the mucube. For a Petrial mucube of unit side length its vertices take on the coordinates

• $(i, j, k)$,

where i, j, k are any three integers.

External links

• jan Misali (2020). "there are 48 regular polyhedra".

Bibliography

• McMullen, Peter; Schulte, Egon (1997). "Regular Polytopes in Ordinary Space" (PDF). Discrete Computational Geometry (47): 449–478. doi:10.1007/PL00009304.