Great enneagrammic retroprism

The great enneagrammic retroprism, or gisterp, also called the great enneagrammic crossed antiprism, is a prismatic uniform polyhedron. It consists of 18 triangles and 2 great enneagrams. Each vertex joins one great enneagram and three triangles. As the name suggests, it is a crossed antiprism based on a great enneagram, seen as a 9/5-gon rather than 9/4.

Vertex coordinates
The vertices of a great enneagrammic retroprism, centered at the origin and with edge length 2sin(4π/9), are given by the following points, as well as their central inversions: where $$H=\sqrt{\frac{1-2\cos\frac{4\pi}9}{2-2\cos\frac{4\pi}9}}\sin\frac{4\pi}9.$$
 * $$\left(1,\,0,\,H\right),$$
 * $$\left(\cos\left(\frac{2\pi}9\right),\,±\sin\left(\frac{2\pi}9\right),\,H\right),$$
 * $$\left(\cos\left(\frac{4\pi}9\right),\,±\sin\left(\frac{4\pi}9\right),\,H\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}2,\,H\right),$$
 * $$\left(\cos\left(\frac{8\pi}9\right),\,±\sin\left(\frac{8\pi}9\right),\,H\right),$$