# Petrial cube

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Petrial cube
Rank3
TypeRegular polytope
Notation
Schläfli symbol${\displaystyle \{4,3\}^\pi}$
${\displaystyle \{6,3\}_4}$
${\displaystyle \{6,3\mid *3\}}$
Elements
Faces4 skew hexagons
Edges12
Vertices8
Related polytopes
ArmyCube
RegimentCube
Dualdouble cover of tetrahedron (degenerate)
Petrie dualCube
Convex hullCube
Abstract properties
Flag count48
Net count6
Euler characteristic0
Schläfli type{6,3}
Topological properties
SurfaceTorus
OrientableYes
Genus1

The Petrial cube is a regular skew polyhedron. It consists of 4 skew hexagons, and it is the Petrie dual of the cube. It has a Euler characteristic of 0.

## Vertex coordinates

The coordinates for the vertices of a Petrial cube with unit side length are the same of that as a cube, being located at ${\displaystyle \left(\pm\frac12,\,\pm\frac12,\,\pm\frac12\right).}$

## Related polyhedra

The rectification of the petrial cube is the octahemioctahedron, which is uniform.