Decagonal-snub cubic duoprism

The decagonal-snub cubic duoprism or dasnic is a convex uniform duoprism that consists of 10 snub cubic prisms, 6 square-decagonal duoprisms, and 32 triangular-decagonal duoprisms of two kinds. Each vertex joins 2 snub cubic prisms, 4 triangular-decagonal duoprisms, and 1 square-decagonal duoprism.

Vertex coordinates
The vertices of a decagonal-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
 * $$\left(0,\,±\frac{1+\sqrt5}2,\,c_1,\,c_2,\,c_3\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,c_1,\,c_2,\,c_3\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,c_1,\,c_2,\,c_3\right),$$
 * $$c_1=\sqrt{\frac{1}{12}\left(4-\sqrt[3]{17+3\sqrt{33}}-\sqrt[3]{17-3\sqrt{33}}\right)},$$
 * $$c_2=\sqrt{\frac{1}{12}\left(2+\sqrt[3]{17+3\sqrt{33}}+\sqrt[3]{17-3\sqrt{33}}\right)},$$
 * $$c_3=\sqrt{\frac{1}{12}\left(4+\sqrt[3]{199+3\sqrt{33}}+\sqrt[3]{199-3\sqrt{33}}\right)}.$$