Petrial tetrahedron

The Petrial tetrahedron is a regular skew polyhedron. It is composed of 3 skew squares.

Hemicube
The hemicube is an abstract polytope isomorphic to the Petrial tetrahedron. It is a tiling of the projective plane. It can be seen as a cube with antipodal points identified. The hemicube is also related to the triangular hosohedron, as if the opposite edges and vertices of each square are identified, the result is a triangular hosohedron.