Heptagonal-snub cubic duoprism

The heptagonal-snub cubic duoprism or hesnic is a convex uniform duoprism that consists of 7 snub cubic prisms, 6 square-heptagonal duoprisms and 32 triangular-heptagonal duoprisms of two kinds. Each vertex joins 2 snub cubic prisms, 4 triangular-heptagonal duoprisms, and 1 square-heptagonal duoprism.

Vertex coordinates
The vertices of a heptagonal-snub cubic duoprism of edge length 2sin(π/7) 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
 * $$\left(1,\,0,\,2c_1\sin\frac\pi7,\,2c_2\sin\frac\pi7,\,2c_3\sin\frac\pi7\right),$$
 * $$\left(\cos\left(\frac{j\pi}7\right),\,±\sin\left(\frac{j\pi}7\right),\,2c_1\sin\frac\pi7,\,2c_2\sin\frac\pi7,\,2c_3\sin\frac\pi7\right),$$
 * j = 2, 4, 6,
 * $$c_1=\sqrt{\frac{1}{12}\left(4-\sqrt[3]{17+3\sqrt{33}}-\sqrt[3]{17-3\sqrt{33}}\right)},$$
 * $$c_2=\sqrt{\frac{1}{12}\left(2+\sqrt[3]{17+3\sqrt{33}}+\sqrt[3]{17-3\sqrt{33}}\right)},$$
 * $$c_3=\sqrt{\frac{1}{12}\left(4+\sqrt[3]{199+3\sqrt{33}}+\sqrt[3]{199-3\sqrt{33}}\right)}.$$