Cuboctahedron atop truncated cube

Cuboctahedron atop truncated cube, or coatic, is a CRF segmentochoron (designated K-4.129 on Richard Klitzing's list). As the name suggests, it consists of a cuboctahedron and a truncated cube as bases, connected by 8 triangular prisms and 6 square cupolas.

It can be obtained as a cap of the small rhombated icositetrachoron, with a cuboctahedron on top.

Vertex coordinates
The vertices of a cuboctahedron atop truncated cube segmentochoron of edge length 1 are given by:
 * (±$\sqrt{2}$/2, ±$\sqrt{2}$/2, 0, 1/2) and all permutations of first three coordinates
 * (±(1+$\sqrt{2+√2}$)/2, ±(1+$\sqrt{4+2√2}$)/2, ±1/2, 0) and all permutations of first three coordinaets