Enneagonal-great rhombicuboctahedral duoprism

The enneagonal-great rhombicuboctahedral duoprism or egirco is a convex uniform duoprism that consists of 9 great rhombicuboctahedral prisms, 6 octagonal-enneagonal duoprisms, 8 hexagonal-enneagonal duoprisms, and 12 square-enneagonal duoprisms. Each vertex joins 2 great rhombicuboctahedral prisms, 1 square-enneagonal duoprism, 1 hexagonal-enneagonal duoprism, and 1 octagonal-enneagonal duoprism.

Vertex coordinates
The vertices of an enneagonal-great rhombicuboctahedral duoprism of edge length 2sin(π/9) are given by all permutations of the last three coordinates of: where j = 2, 4, 8.
 * $$\left(1,\,0,\,±(1+2\sqrt2)\sin\frac\pi9,\,±(1+\sqrt2)\sin\frac\pi9,\,±\sin\frac\pi9\right),$$
 * $$\left(\cos\left(\frac{j\pi}9\right),\,±\sin\left(\frac{j\pi}9\right),\,±(1+2\sqrt2)\sin\frac\pi9,\,±(1+\sqrt2)\sin\frac\pi9,\,±\sin\frac\pi9\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}2,\,±(1+2\sqrt2)\sin\frac\pi9,\,±(1+\sqrt2)\sin\frac\pi9,\,±\sin\frac\pi9\right),$$