Chamfered tetrahedron

The chamfered tetrahedron is a modification of the tetrahedron that can have one edge length but has irregular faces. It has 4 triangles and 6 hexagons 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.

The hexagonal faces have angles of 90° on one pair of opposite vertices, and angles of 135° on the four remaining vertices.

It can be modified such that it has a single inradius, or such that it has a single midradius or "edge radius." The latter version is called the "canonical" version.

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