Pentagrammic-great enneagrammic duoprism

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

Vertex coordinates
The coordinates of a pentagrammic-great enneagrammic duoprism, centered at the origin and with edge length 2sin(4π/9), are given by: where j = 2, 4, 8.
 * $$\left(±\sin\frac{4\pi}{9},\,-\sqrt{\frac{5-2\sqrt5}{5}}\sin\frac{4\pi}{9},\,1,\,0\right),$$
 * $$\left(±\sin\frac{4\pi}{9},\,-\sqrt{\frac{5-2\sqrt5}{5}}\sin\frac{4\pi}{9},\,\cos\left(\frac{j\pi}{9}\right),\,±\sin\left(\frac{j\pi}{9}\right)\right),$$
 * $$\left(±\sin\frac{4\pi}{9},\,-\sqrt{\frac{5-2\sqrt5}{5}}\sin\frac{4\pi}{9},\,-\frac12,\,±\frac{\sqrt3}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2}\sin\frac{4\pi}{9},\,\sqrt{\frac{5+\sqrt5}{10}}\sin\frac{4\pi}{9},\,1,\,0\right),$$
 * $$\left(±\frac{\sqrt5-1}{2}\sin\frac{4\pi}{9},\,\sqrt{\frac{5+\sqrt5}{10}}\sin\frac{4\pi}{9},\,\cos\left(\frac{j\pi}{9}\right),\,±\sin\left(\frac{j\pi}{9}\right)\right),$$
 * $$\left(±\frac{\sqrt5-1}{2}\sin\frac{4\pi}{9},\,\sqrt{\frac{5+\sqrt5}{10}}\sin\frac{4\pi}{9},\,-\frac12,\,±\frac{\sqrt3}{2}\right),$$
 * $$\left(0,\,-2\sqrt{\frac{5-\sqrt5}{10}}\sin\frac{4\pi}{9},\,1,\,0\right),$$
 * $$\left(0,\,-2\sqrt{\frac{5-\sqrt5}{10}}\sin\frac{4\pi}{9},\,\cos\left(\frac{j\pi}{9}\right),\,±\sin\left(\frac{j\pi}{9}\right)\right),$$
 * $$\left(0,\,-2\sqrt{\frac{5-\sqrt5}{10}}\sin\frac{4\pi}{9},\,-\frac12,\,±\frac{\sqrt3}{2}\right),$$