Enneagonal-dodecagrammic duoprism

The enneagonal-dodecagrammic duoprism, also known as the 9-12/5 duoprism, is a uniform duoprism that consists of 12 enneagonal prisms and 9 dodecagrammic prisms, with 2 of each at each vertex.

Vertex coordinates
The coordinates of a enneagonal-dodecagrammic duoprism, centered at the origin and with edge length 2sin(π/9), are given by: where j = 2, 4, 8.
 * $$\left(1,\,0,\,±\left(\sqrt3-1\right)\sin\frac{\pi}9,\,±\left(\sqrt3-1\right)\sin\frac{\pi}9\right),$$
 * $$\left(1,\,0,\,±\sin\frac{\pi}9,\,±\left(2-\sqrt3\right)\sin\frac{\pi}9\right),$$
 * $$\left(1,\,0,\,±\left(2-\sqrt3\right)\sin\frac{\pi}9,\,±\sin\frac{\pi}9\right),$$
 * $$\left(\cos\left(\frac{j\pi}9\right),\,±\sin\left(\frac{j\pi}9\right),\,±\left(\sqrt3-1\right)\sin\frac{\pi}9,\,±\left(\sqrt3-1\right)\sin\frac{\pi}9\right),$$
 * $$\left(\cos\left(\frac{j\pi}9\right),\,±\sin\left(\frac{j\pi}9\right),\,±\sin\frac{\pi}9,\,±\left(2-\sqrt3\right)\sin\frac{\pi}9\right),$$
 * $$\left(\cos\left(\frac{j\pi}9\right),\,±\sin\left(\frac{j\pi}9\right),\,±\left(2-\sqrt3\right)\sin\frac{\pi}9,\,±\sin\frac{\pi}9\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}2,\,±\left(\sqrt3-1\right)\sin\frac{\pi}9,\,±\left(\sqrt3-1\right)\sin\frac{\pi}9\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}2,\,±\sin\frac{\pi}9,\,±\left(2-\sqrt3\right)\sin\frac{\pi}9\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}2,\,±\left(2-\sqrt3\right)\sin\frac{\pi}9,\,±\sin\frac{\pi}9\right),$$