Hexagonal-snub cubic duoprism

The hexagonal-snub cubic duoprism or hasnic is a convex uniform duoprism that consists of 6 snub cubic prisms, 6 square-hexagonal duoprisms and 32 triangular-hexagonal duoprisms of two kinds. Each vertex joins 2 snub cubic prisms, 4 triangular-hexagonal duoprisms, and 1 square-hexagonal duoprism.

Vertex coordinates
The vertices of a hexagonal-snub cubic duoprism of edge length 1 are given by by all even permutations with an even number of sign changes, plus all odd permutations with an odd amount of sign changes, of the last three coordinates of: where
 * $$\left(0,\,±1,\,c_1,\,c_2,\,c_3\right),$$
 * $$\left(±\frac{\sqrt3}2,\,±\frac12,\,c_1,\,c_2,\,c_3\right),$$
 * $$c_1=\sqrt{\frac{1}{12}\left(4-\sqrt[3]{17+3\sqrt{33}}-\sqrt[3]{17-3\sqrt{33}}\right)},$$
 * $$c_2=\sqrt{\frac{1}{12}\left(2+\sqrt[3]{17+3\sqrt{33}}+\sqrt[3]{17-3\sqrt{33}}\right)},$$
 * $$c_3=\sqrt{\frac{1}{12}\left(4+\sqrt[3]{199+3\sqrt{33}}+\sqrt[3]{199-3\sqrt{33}}\right)}.$$