Enneagonal-truncated octahedral duoprism

The enneagonal-truncated octahedral duoprism or etoe is a convex uniform duoprism that consists of 9 truncated octahedral prisms, 8 hexagonal-enneagonal duoprisms, and 6 square-enneagonal duoprisms. Each vertex joins 2 truncated octahedral prisms, 1 square-enneagonal duoprism, and 2 hexagonal-enneagonal duoprisms.

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