Chamfered tetrahedron

The chamfered tetrahedron is a modification of the tetrahedron that can have one edge length but has irregular faces. It has 6 hexagons with 180° rotational symmetry and 4 triangles as faces, and 4 order-3 vertices that can be thought of as coming from the tetrahedron as well as 12 new order-3 vertices.

A "canonical" version can also be constructed that has a single midradius or "edge radius."

It can also be obtained by truncating alternate vertices of a cube, and can also be viewed as a tetrahedrally-symmetric Goldberg polyhedron.