Hendecagonal-great rhombicosidodecahedral duoprism

The hendecagonal-great rhombicosidodecahedral duoprism or hengrid is a convex uniform duoprism that consists of 11 great rhombicosidodecahedral prisms, 12 decagonal-hendecagonal duoprisms, 20 hexagonal-hendecagonal duoprisms, and 30 square-hendecagonal duoprisms. Each vertex joins 2 great rhombicosidodecahedral prisms, 1 square-hendecagonal duoprism, 1 hexagonal-hendecagonal duoprism, and 1 decagonal-hendecagonal duoprism.

Vertex coordinates
The vertices of a hendecagonal-great rhombicosidodecahedral duoprism of edge length 2sin(π/11) are given by all permutations of the last three coordinates of: along with all even permutations of the last three coordinates of: where j = 2, 4, 6, 8, 10.
 * $$\left(1,\,0,\,±\sin\frac\pi{11},\,±\sin\frac\pi{11},\,(3+2\sqrt5)\sin\frac\pi{11}\right),$$
 * $$\left(\cos\left(\frac{j\pi}{11}\right),\,±\sin\left(\frac{j\pi}{11}\right),\,±\sin\frac\pi{11},\,±\sin\frac\pi{11},\,(3+2\sqrt5)\sin\frac\pi{11}\right),$$
 * $$\left(1,\,0,\,±\sin\frac\pi{11},\,±(2+\sqrt5)\sin\frac\pi{11},\,±(4+\sqrt5)\sin\frac\pi{11}\right),$$
 * $$\left(\cos\left(\frac{j\pi}{11}\right),\,±\sin\left(\frac{j\pi}{11}\right),\,±\sin\frac\pi{11},\,±(2+\sqrt5)\sin\frac\pi{11},\,±(4+\sqrt5)\sin\frac\pi{11}\right),$$
 * $$\left(1,\,0,\,±2\sin\frac\pi{11},\,±\frac{(3+\sqrt5)\sin\frac\pi{11}}2,\,±\frac{(7+3\sqrt5)\sin\frac\pi{11}}2\right),$$
 * $$\left(\cos\left(\frac{j\pi}{11}\right),\,±\sin\left(\frac{j\pi}{11}\right),\,±2\sin\frac\pi{11},\,±\frac{(3+\sqrt5)\sin\frac\pi{11}}2,\,±\frac{(7+3\sqrt5)\sin\frac\pi{11}}2\right),$$
 * $$\left(1,\,0,\,±\frac{(3+\sqrt5)\sin\frac\pi{11}}2,\,±3\frac{(1+\sqrt5)\sin\frac\pi{11}}2,\,±(3+\sqrt5)\sin\frac\pi{11}\right),$$
 * $$\left(\cos\left(\frac{j\pi}{11}\right),\,±\sin\left(\frac{j\pi}{11}\right),\,±\frac{(3+\sqrt5)\sin\frac\pi{11}}2,\,±3\frac{(1+\sqrt5)\sin\frac\pi{11}}2,\,±(3+\sqrt5)\sin\frac\pi{11}\right),$$
 * $$\left(1,\,0,\,±(1+\sqrt5)\sin\frac\pi{11},\,±\frac{(5+3\sqrt5)\sin\frac\pi{11}}2,\,±\frac{(5+\sqrt5)\sin\frac\pi{11}}2\right),$$
 * $$\left(\cos\left(\frac{j\pi}{11}\right),\,±\sin\left(\frac{j\pi}{11}\right),\,±(1+\sqrt5)\sin\frac\pi{11},\,±\frac{(5+3\sqrt5)\sin\frac\pi{11}}2,\,±\frac{(5+\sqrt5)\sin\frac\pi{11}}2\right),$$