Square-snub cubic duoprism

The square-snub cubic duoprism or squasnic is a convex uniform duoprism that consists of 4 snub cubic prisms, 6 tesseracts and 32 triangular-square duoprisms of two kinds.

Vertex coordinates
The vertices of a square-snub cubic duoprism of edge length 1 are given by all even permutations with an even number of sign changes, plus all odd permutations with an odd amount of sign changes excluding the last coordinate of
 * (±1/2, ±1/2, c1, c2, c3)

where


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