Petrial mutetrahedron

Petrial mutetrahedron
Rank	3
Space	Spherical
Notation
Schläfli symbol	$\{6,6\mid 3\}^\pi$ $\{\infty,6\}_{6,3}$
Elements
Faces	$N$ triangular helices
Edges	$N\times 3M$
Vertices	$N\times M$
Vertex figure	Skew hexagon
Petrie polygons	$N\times M$ hexagons
Related polytopes
Army	Batatoh
Regiment	Batatoh
Petrie dual	Mutetrahedron
Abstract properties
Flag count	$N\times 12M$
Schläfli type	{∞,6}
Properties
Convex	No

The Petrial mutetrahedron is a regular skew apeirohedron in 3-dimensional Euclidean space. It is the Petrie dual of the mutetrahedron, and it has 6 triangular helices meeting at a vertex.

Vertex coordinates

The petrial mutetrahedron's coordinates are the same as the mutetrahedron and therefore the cyclotruncated tetrahedral-octahedral honeycomb.

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.