Hendecagonal-great rhombicuboctahedral duoprism

The hendecagonal-great rhombicuboctahedral duoprism or hengirco is a convex uniform duoprism that consists of 11 great rhombicuboctahedral prisms, 6 octagonal-hendecagonal duoprisms, 8 hexagonal-hendecagonal duoprisms, and 12 square-hendecagonal duoprisms. Each vertex joins 2 great rhombicuboctahedral prisms, 1 square-hendecagonal duoprism, 1 hexagonal-hendecagonal duoprism, and 1 octagonal-hendecagonal duoprism.

Vertex coordinates
The vertices of a hendecagonal-great rhombicuboctahedral duoprism of edge length 2sin(π/11) are given by all permutations of the last three coordinates of: where j = 2, 4, 6, 8, 10.
 * $$\left(1,\,0,\,±(1+2\sqrt2)\sin\frac\pi{11},\,±(1+\sqrt2)\sin\frac\pi{11},\,±\sin\frac\pi{11}\right),$$
 * $$\left(\cos\left(\frac{j\pi}{11}\right),\,±\sin\left(\frac{j\pi}{11}\right),\,±(1+2\sqrt2)\sin\frac\pi{11},\,±(1+\sqrt2)\sin\frac\pi{11},\,±\sin\frac\pi{11}\right),$$