Pentagonal-snub cubic duoprism

The pentagonal-snub cubic duoprism or pesnic is a convex uniform duoprism that consists of 5 snub cubic prisms, 6 square-pentagonal duoprisms, and 32 triangular-pentagonal duoprisms of two kinds. Each vertex joins 2 snub cubic prisms, 4 triangular-pentagonal duoprisms, and 1 square-pentagonal duoprism.

Vertex coordinates
The vertices of a pentagonal-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
 * $$\left(0,\, \sqrt{\frac{5+\sqrt5}{10}},\,c_1,\,c_2,\,c_3\right),$$
 * $$\left(±\frac{1+\sqrt5}4,\, \sqrt{\frac{5-\sqrt5}{40}},\,c_1,\,c_2,\,c_3\right),$$
 * $$\left(±\frac12,\, -\sqrt{\frac{5+2\sqrt5}{20}},\,c_1,\,c_2,\,c_3\right),$$
 * $$c_1=\sqrt{\frac{1}{12}\left(4-\sqrt[3]{17+3\sqrt{33}}-\sqrt[3]{17-3\sqrt{33}}\right)},$$
 * $$c_2=\sqrt{\frac{1}{12}\left(2+\sqrt[3]{17+3\sqrt{33}}+\sqrt[3]{17-3\sqrt{33}}\right)},$$
 * $$c_3=\sqrt{\frac{1}{12}\left(4+\sqrt[3]{199+3\sqrt{33}}+\sqrt[3]{199-3\sqrt{33}}\right)}.$$