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, which can be obtained by attaching 8 of these segmentochora to the truncated cubic cells of the prismatorhombated hexadecachoron.

Vertex coordinates
The vertices of a cuboctahedron atop truncated cube segmentochoron of edge length 1 are given by:
 * $$\left(±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0,\,\frac12\right)$$ and all permutations of first three coordinates
 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac12,\,0\right)$$ and all permutations of first three coordinates