Petrial cube

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 the Petrial cube is the same of that as the cube, being located at$$\left(±\frac{1}{2},\,±\frac{1}{2},\,±\frac{1}{2}\right).$$