Petrial cube

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Petrial cube
Petrial cube.gif
Rank3
TypeRegular polytope
Notation
Schläfli symbol

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[edit | edit source]

The coordinates for the vertices of a Petrial cube with unit side length are the same of that as a cube, being located at

Related polyhedra[edit | edit source]

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

External links[edit | edit source]