Hendecagonal-icosidodecahedral duoprism

The hendecagonal-icosidodecahedral duoprism or henid is a convex uniform duoprism that consists of 11 icosidodecahedral prisms, 12 pentagonal-hendecagonal duoprisms and 20 triangular-hendecagonal duoprisms. Each vertex joins 2 icosidodecahedral prisms, 2 triangular-hendecagonal duoprisms, and 2 pentagonal-hendecagonal duoprisms.

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