# Skewed Petrial muoctahedron

Skewed Petrial muoctahedron
Rank3
TypeRegular
Notation
Schläfli symbol${\displaystyle \{6,4\}_{6}}$
${\displaystyle \left\{{\dfrac {6}{1,3}},4:{\dfrac {6}{1,3}}\right\}}$
Elements
Faces2N  skew hexagons
Edges6N
Vertices3N
Vertex figureSquare
Petrie polygons2N  skew hexagons
HolesApeirogons
Related polytopes
RegimentSkewed muoctahedron
DualPetrial halved mucube
Petrie dualSkewed Petrial muoctahedron
Abstract & topological properties
Schläfli type{6,4}
OrientableYes
Genus
Properties
ConvexNo
Dimension vector(1,2,1)

The skewed Petrial muoctahedron is a regular skew polyhedron in 3-dimensional Euclidean space.

## 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.

## Related polytopes

As its name suggests, it can be constructed as the skewing of the Petrial muoctahedron. It follows from the definition of skewing that it, can also be constructed as the dual of the Petrial halved mucube.

It can be constructed as the rectification of the mutetrahedron, by applying a generalized Wythoffian construction. The geometric construction, (i.e. placing a vertex at the midpoints of edges etc.) yields a different non-regular polytope.