Skewed Petrial muoctahedron

Skewed Petrial muoctahedron
Rank	3
Type	Regular
Notation
Schläfli symbol	$\{6,4\}_{6}$ $\left\{{\dfrac {6}{1,3}},4:{\dfrac {6}{1,3}}\right\}$
Elements
Faces	2N  skew hexagons
Edges	6N
Vertices	3N
Vertex figure	Square
Petrie polygons	2N  skew hexagons
Holes	Apeirogons
Related polytopes
Regiment	Skewed muoctahedron
Dual	Petrial halved mucube
Petrie dual	Skewed Petrial muoctahedron
Abstract & topological properties
Schläfli type	{6,4}
Orientable	Yes
Genus	∞
Properties
Convex	No
Dimension vector	(2,1,2)

The skewed Petrial muoctahedron is a regular skew polyhedron in 3-dimensional Euclidean space. It can be constructed as the skewing of the Petrial muoctahedron, or as the dual of the Petrial halved mucube.

Vertex coordinates

The vertex coordinates of a skewed Petrial muoctahedron with unit edge length can be given as:

• $(i,j,k)$,

where two or more of i , j  and k  are odd.

Gallery

• 

  A vertex of the skewed Petrial muoctahedron (red) and all adjacent faces. Each face is shown with transparent membrane to assist in depth perception.

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.