Great enneagrammic antiprism

The great enneagrammic antiprism, or gisteap, 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 an antiprism based on a great enneagram.

Vertex coordinates
The vertex coordinates of a great enneagrammic antiprism with edge length 2sin(4π/9) are given by: where $$H=\sqrt{\frac{1+2\cos\frac{4\pi}9}{2+2\cos\frac{4\pi}9}}\sin\frac{4\pi}9.$$
 * $$\left(1,\,0,\,±H\right),$$
 * $$\left(\cos\left(\frac{2\pi}{9}\right),\,±\sin\left(\frac{2\pi}{9}\right),\,±H\right),$$
 * $$\left(\cos\left(\frac{4\pi}{9}\right),\,±\sin\left(\frac{4\pi}{9}\right),\,±H\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}{2},\,±H\right),$$
 * $$\left(\cos\left(\frac{8\pi}{9}\right),\,±\sin\left(\frac{8\pi}{9}\right),\,±H\right),$$