Enneagrammic-great enneagrammic duoprism

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

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