Truncated cuboctahedron

Note that the name truncated cuboctahedron may be a little misleading, if you truncate a cuboctahedron by cutting the corners off, you (according to my intuition) do not get an actual regular truncated cuboctahedron, you get something similar, just with rectangles instead of squares, and either the hexagons or octagons will also not be regular.

Canonical coordinates for the vertices of a truncated cuboctahedron centered at the origin are all permutations of (±1, ±(1+√2), ±(1+√8)).

It has 12 regular square faces, 8 regular hexagonal faces, 6 regular octagonal faces, 48 vertices and 72 edges.

See cube, octahedron, cuboctahedron, (small) rhombicuboctahedron.