Chamfered octahedron

The chamfered octahedron is a modification of the octahedron that can have one edge length but has irregular faces. It has 8 triangles and 12 hexagons as faces, and 6 order-4 vertices that can be thought of as coming from the octahedron as well as 24 new order-3 vertices.

The hexagonal faces have angles of $$\arccos\left(\frac13\right) ≈ 70.52878^\circ$$ on one pair of opposite vertices, and angles of $$\arccos\left(-\sqrt{\frac23}\right) ≈ 144.73561^\circ$$ 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 viewed as an order-3-truncated rhombic dodecahedron, or as an octahedrally-symmetric Goldberg polyhedron.