Hendecagonal-snub cubic duoprism

4 The hendecagonal-snub cubic duoprism or hensnic is a convex uniform duoprism that consists of 11 snub cubic prisms, 6 square-hendecagonal duoprisms, and 32 triangular-hendecagonal duoprisms of two kinds. Each vertex joins 2 snub cubic prisms, 4 triangular-hendecagonal duoprisms, and 1 square-hendecagonal duoprism.

Vertex coordinates
The vertices of a hendecagonal-snub cubic duoprism of edge length 2sin(π/11) 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
 * $$\left(1,\,0,\,2c_1\sin\frac\pi{11},\,2c_2\sin\frac\pi{11},\,2c_3\sin\frac\pi{11}\right),$$
 * $$\left(\cos\left(\frac{j\pi}{11}\right),\,±\sin\left(\frac{j\pi}{11}\right),\,2c_1\sin\frac\pi{11},\,2c_2\sin\frac\pi{11},\,2c_3\sin\frac\pi{11}\right),$$
 * j = 2, 4, 6, 8, 10,
 * $$c_1=\sqrt{\frac{1}{12}\left(4-\sqrt[3]{17+3\sqrt{33}}-\sqrt[3]{17-3\sqrt{33}}\right)},$$
 * $$c_2=\sqrt{\frac{1}{12}\left(2+\sqrt[3]{17+3\sqrt{33}}+\sqrt[3]{17-3\sqrt{33}}\right)},$$
 * $$c_3=\sqrt{\frac{1}{12}\left(4+\sqrt[3]{199+3\sqrt{33}}+\sqrt[3]{199-3\sqrt{33}}\right)}.$$