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 are the same of that as the cube, being located at $$\left(±\frac12,\,±\frac12,\,±\frac12\right).$$