Truncated cube atop great rhombicuboctahedron

Truncated cube atop great rhombicuboctahedron is a CRF segmentochoron (designated K-4.128 on Richard Klitzing's list). As the name suggests, it consists of a truncated cube and a great rhombicuboctahedron as bases, connected by 12 triangular prisms, 8 triangular cupolas, and 6 octagonal prisms.

It can be constructed as a cap of the prismatorhombated hexadecachoron, with a truncated cube at the top.

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