Enneagonal-truncated dodecahedral duoprism

The enneagonal-truncated dodecahedral duoprism or etid is a convex uniform duoprism that consists of 9 truncated dodecahedral prisms, 12 enneagonal-decagonal duoprisms and 20 triangular-enneagonal duoprisms. Each vertex joins 2 truncated dodecahedral prisms, 1 triangular-enneagonal duoprism, and 2 enneagonal-decagonal duoprisms.

The vertices of an enneagonal-truncated octahedral duoprism of edge length 2sin(π/9) are given by all even permutations of the last three coordinates of: where j = 2, 4, 8.
 * $$\left(1,\,0,\,0,\,±\sin\frac\pi9,\,±\frac{(5+3\sqrt5)\sin\frac\pi9}2\right),$$
 * $$\left(1,\,0,\,±\sin\frac\pi9,\,±\frac{(3+\sqrt5)\sin\frac\pi9}2,\,±(3+\sqrt5)\sin\frac\pi9\right),$$
 * $$\left(1,\,0,\,±\frac{(3+\sqrt5)\sin\frac\pi9}2,\,±(1+\sqrt5)\sin\frac\pi9,\,±(2+\sqrt5)\sin\frac\pi9\right),$$
 * $$\left(\cos\left(\frac{j\pi}9\right),\,±\sin\left(\frac{j\pi}9\right),\,0,\,±\sin\frac\pi9,\,±\frac{(5+3\sqrt5)\sin\frac\pi9}2\right),$$
 * $$\left(\cos\left(\frac{j\pi}9\right),\,±\sin\left(\frac{j\pi}9\right),\,±\sin\frac\pi9,\,±\frac{(3+\sqrt5)\sin\frac\pi9}2,\,±(3+\sqrt5)\sin\frac\pi9\right),$$
 * $$\left(\cos\left(\frac{j\pi}9\right),\,±\sin\left(\frac{j\pi}9\right),\,±\frac{(3+\sqrt5)\sin\frac\pi9}2,\,±(1+\sqrt5)\sin\frac\pi9,\,±(2+\sqrt5)\sin\frac\pi9\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}2,\,0,\,±\sin\frac\pi9,\,±\frac{(5+3\sqrt5)\sin\frac\pi9}2\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}2,\,±\sin\frac\pi9,\,±\frac{(3+\sqrt5)\sin\frac\pi9}2,\,±(3+\sqrt5)\sin\frac\pi9\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}2,\,±\frac{(3+\sqrt5)\sin\frac\pi9}2,\,±(1+\sqrt5)\sin\frac\pi9,\,±(2+\sqrt5)\sin\frac\pi9\right),$$