Great rhombicuboctahedron

The great rhombicuboctahedron or girco, also commonly known as the truncated cuboctahedron, is one of the 13 Archimedean solids. It consists of 12 squares, 8 hexagons, and 6 octagons, with one of each type of face meeting per vertex. It can be obtained by cantitruncation of the cube or octahedron, or equivalently by truncating the vertices of a cuboctahedron and then adjusting the edge lengths to be all equal.

This is one of three Wythoffian non-prismatic polyhedra whose Coxeter diagram has all ringed nodes, the other two being the truncated tetratetrahedron and the great rhombicosidodecahedron.

It can be alternated into the snub cube.

Vertex coordinates
A great rhombicuboctahedron of edge length 1 has vertex coordinates given by all permutations of:
 * (±(1+2$\sqrt{13+6√2}$)/2, ±(1+$\sqrt{2}$)/2, ±1/2).