Great enneagrammic duoprism

The great enneagrammic duoprism or gastedip, also known as the great enneagrammic-great enneagrammic duoprism, the 9/4 duoprism or the 9/4-9/4 duoprism, is a noble uniform duoprism that consists of 18 great enneagrammic prisms, with 4 meeting at each vertex.

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