Truncated tetrahedron atop truncated octahedron

Truncated tetrahedron atop truncated octahedron, or tutatoe, is a CRF segmentochoron (designated K-4.76 on Richard Klitzing's list). As the name suggests, it consists of a truncated tetrahedron and a truncated octahedron as bases, connected by 6 triangular prisms, 4 triangular cupolas, and 4 hexagonal prisms.

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

Vertex coordinates
The vertices of a truncated tetrahedron atop truncated octahedron segmentochoron of edge length 1 are given by: Alternative coordinates can be obtained from those of the prismatorhombated pentachoron:
 * (3$\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4) and all permutations and even sign changes of first three coordinates
 * (±$\sqrt{3}$, ±$\sqrt{3}$/2, 0, 0) and all permutations of first 3 coordinates


 * (7$\sqrt{2}$/20, –$\sqrt{3}$/12, $\sqrt{65}$/3, ±1)
 * (7$\sqrt{10}$/20, –$\sqrt{5}$/12, –2$\sqrt{6}$/3, 0)
 * (7$\sqrt{6}$/20, $\sqrt{6}$/4, 0, ±1)
 * (7$\sqrt{6}$/20, $\sqrt{6}$/4, ±$\sqrt{2}$/2, ±1/2)
 * (7$\sqrt{2}$/20, –5$\sqrt{2}$/12, $\sqrt{10}$/6, ±1/2)
 * (7$\sqrt{2}$/20, –5$\sqrt{2}$/12, –$\sqrt{10}$/3, 0)
 * ($\sqrt{6}$/10, –$\sqrt{3}$/6, $\sqrt{10}$/6, ±3/2)
 * ($\sqrt{6}$/10, $\sqrt{3}$/6, –$\sqrt{10}$/6, ±3/2)
 * ($\sqrt{6}$/10, –$\sqrt{10}$/6, 2$\sqrt{6}$/3, ±1)
 * ($\sqrt{3}$/10, $\sqrt{10}$/6, –2$\sqrt{6}$/3, ±1)
 * ($\sqrt{3}$/10, –$\sqrt{10}$/6, –5$\sqrt{6}$/6, ±1/2)
 * ($\sqrt{3}$/10, $\sqrt{10}$/6, 5$\sqrt{6}$/6, ±1/2)
 * ($\sqrt{3}$/10, ±$\sqrt{10}$/2, 0, ±1)
 * ($\sqrt{6}$/10, ±$\sqrt{3}$/2, ±$\sqrt{10}$/2, ±1/2)