Truncated octahedron atop truncated cube

Truncated octahedron atop truncated cube, or toatic, is a CRF segmentochoron (designated K-4.98 on Richard Klitzing's list). As the name suggests, it consists of a truncated octahedron and a truncated cube as bases, connected by 12 tetrahedra, 8 triangular cupolas, and 6 square cupolas.

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