Snub cubic prism

The snub cubic prism or sniccup is a prismatic uniform polychoron that consists of 2 snub cubes, 6 cubes, and 8+24 triangular prisms. Each vertex joins 1 snub cube, 1 cube, and 4 triangular prisms. As the name suggests, it is a prism based on the snub cube. As such it is also a convex segmentochoron (designated K-4.60 on Richard Klitzing's list).

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
 * $$\left(c_1,\,c_2,\,c_3,\,±\frac12\right),$$
 * $$c_1=\sqrt{\frac{1}{12}\left(4-\sqrt[3]{17+3\sqrt{33}}-\sqrt[3]{17-3\sqrt{33}}\right)},$$
 * $$c_2=\sqrt{\frac{1}{12}\left(2+\sqrt[3]{17+3\sqrt{33}}+\sqrt[3]{17-3\sqrt{33}}\right)},$$
 * $$c_3=\sqrt{\frac{1}{12}\left(4+\sqrt[3]{199+3\sqrt{33}}+\sqrt[3]{199-3\sqrt{33}}\right)}.$$