Enneagonal-truncated icosahedral duoprism

The enneagonal-truncated icosahedral duoprism or eti is a convex uniform duoprism that consists of 9 truncated icosahedral prisms, 20 hexagonal-enneagonal duoprisms and 12 pentagonal-enneagonal duoprisms. Each vertex joins 2 truncated icosahedral prisms, 1 pentagonal-enneagonal duoprism, and 2 hexagonal-enneagonal duoprisms.

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