Snub cubic prism

The snub cubic prism or sniccup is one of the uniform polychora made as the prism product of a uniform polyhedron and a dyad that consists of 2 snub cubes, 6 cubes, and 32 triangular prisms of two kinds.

This polychoron can be alternated into an omnisnub dodecahedral antiprism, although it cannot be made uniform.

Vertex coordinates
The vertices of a snub cubic prism of edge length 1 are given by all even permutations and even sign changes, as well as odd permutations and odd sign changes of the first three coordinates of: where
 * (c1, c2, c3, ±1/2),
 * $$c_1=\sqrt{\frac{1}{12}\left(4-\sqrt[3]{17+3\sqrt{33}}-\sqrt[3]{17-3\sqrt{33}}\right)},$$
 * $$c_2=\sqrt{\frac{1}{12}\left(2+\sqrt[3]{17+3\sqrt{33}}+\sqrt[3]{17-3\sqrt{33}}\right)},$$
 * $$c_3=\sqrt{\frac{1}{12}\left(4+\sqrt[3]{199+3\sqrt{33}}+\sqrt[3]{199-3\sqrt{33}}\right)}.$$