Great enneagrammic-dodecagrammic duoprism

The great enneagrammic-dodecagrammic duoprism, also known as the 9/4-12/5 duoprism, is a uniform duoprism that consists of 12 great enneagrammic prisms and 9 dodecagrammic prisms, with 2 of each at each vertex.

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