Enneagonal-truncated cubic duoprism

The enneagonal-truncated cubic duoprism or etic is a convex uniform duoprism that consists of 9 truncated cubic prisms, 6 octagonal-enneagonal duoprisms and 8 triangular-enneagonal duoprisms. Each vertex joins 2 truncated cubic prisms, 1 triangular-enneagonal duoprism, and 2 octagonal-enneagonal duoprisms.

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