Hendecagonal-truncated dodecahedral duoprism

The hendecagonal-truncated dodecahedral duoprism or hentid is a convex uniform duoprism that consists of 11 truncated dodecahedral prisms, 12 decagonal-hendecagonal duoprisms, and 20 triangular-hendecagonal duoprisms. Each vertex joins 2 truncated dodecahedral prisms, 1 triangular-hendecagonal duoprism, and 2 decagonal-hendecagonal duoprisms.

Vertex coordinates
The vertices of a hendecagonal-truncated dodecahedral duoprism of edge length 2sin(π/11) are given by all even permutations of the last three coordinates of: where j = 2, 4, 6, 8, 10.
 * $$\left(1,\,0,\,0,\,±\sin\frac\pi{11},\,±\frac{(5+3\sqrt5)\sin\frac\pi{11}}2\right),$$
 * $$\left(1,\,0,\,±\sin\frac\pi{11},\,±\frac{(3+\sqrt5)\sin\frac\pi{11}}2,\,±(3+\sqrt5)\sin\frac\pi{11}\right),$$
 * $$\left(1,\,0,\,±\frac{(3+\sqrt5)\sin\frac\pi{11}}2,\,±(1+\sqrt5)\sin\frac\pi{11},\,±(2+\sqrt5)\sin\frac\pi{11}\right),$$
 * $$\left(\cos\left(\frac{j\pi}{11}\right),\,±\sin\left(\frac{j\pi}{11}\right),\,0,\,±\sin\frac\pi{11},\,±\frac{(5+3\sqrt5)\sin\frac\pi{11}}2\right),$$
 * $$\left(\cos\left(\frac{j\pi}{11}\right),\,±\sin\left(\frac{j\pi}{11}\right),\,±\sin\frac\pi{11},\,±\frac{(3+\sqrt5)\sin\frac\pi{11}}2,\,±(3+\sqrt5)\sin\frac\pi{11}\right),$$
 * $$\left(\cos\left(\frac{j\pi}{11}\right),\,±\sin\left(\frac{j\pi}{11}\right),\,±\frac{(3+\sqrt5)\sin\frac\pi{11}}2,\,±(1+\sqrt5)\sin\frac\pi{11},\,±(2+\sqrt5)\sin\frac\pi{11}\right),$$