Enneagonal-snub cubic duoprism

The enneagonal-snub cubic duoprism or esnic is a convex uniform duoprism that consists of 9 snub cubic prisms, 6 square-enneagonal duoprisms, and 32 triangular-enneagonal duoprisms of two kinds. Each vertex joins 2 snub cubic prisms, 4 triangular-enneagonal duoprisms, and 1 square-enneagonal duoprism.

Vertex coordinates
The vertices of an enneagonal-snub cubic duoprism of edge length 2sin(π/9) 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
 * $$\left(1,\,0,\,2c_1\sin\frac\pi9,\,2c_2\sin\frac\pi9,\,2c_3\sin\frac\pi9\right),$$
 * $$\left(\cos\left(\frac{j\pi}9\right),\,±\sin\left(\frac{j\pi}9\right),\,2c_1\sin\frac\pi9,\,2c_2\sin\frac\pi9,\,2c_3\sin\frac\pi9\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}2,\,2c_1\sin\frac\pi9,\,2c_2\sin\frac\pi9,\,2c_3\sin\frac\pi9\right),$$
 * j = 2, 4, 8,
 * $$c_1=\sqrt{\frac{1}{12}\left(4-\sqrt[3]{17+3\sqrt{33}}-\sqrt[3]{17-3\sqrt{33}}\right)},$$
 * $$c_2=\sqrt{\frac{1}{12}\left(2+\sqrt[3]{17+3\sqrt{33}}+\sqrt[3]{17-3\sqrt{33}}\right)},$$
 * $$c_3=\sqrt{\frac{1}{12}\left(4+\sqrt[3]{199+3\sqrt{33}}+\sqrt[3]{199-3\sqrt{33}}\right)}.$$