Pentagonal-great enneagrammic duoprism

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

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