Great enneagrammic-decagrammic duoprism

The great enneagrammic-decagrammic duoprism, also known as gistastadedip or the 9/4-10/3 duoprism, is a uniform duoprism that consists of 10 great enneagrammic prisms and 9 decagrammic prisms, with 2 of each at each vertex.

Coordinates
The vertex coordinates of a great enneagrammic-decagrammic duoprism, centered at the origin and with edge length 2sin(4π/9), are given by: where j, k = 2, 4, 8.
 * $$\left(1,\,0,\,±\sin\frac{4\pi}{9},\,±\sqrt{5-2\sqrt5}\sin\frac{4\pi}{9}\right),$$
 * $$\left(1,\,0,\,±\frac{3-\sqrt5}{2}\sin\frac{4\pi}{9},\,±\sqrt{\frac{5-\sqrt5}{2}}\sin\frac{4\pi}{9}\right),$$
 * $$\left(1,\,0,\,±\left(\sqrt5-1\right)\sin\frac{4\pi}{9},\,0\right),$$
 * $$\left(\cos\left(\frac{j\pi}{9}\right),\,±\sin\left(\frac{j\pi}{9}\right),\,±\sin\frac{4\pi}{9},\,±\sqrt{5-2\sqrt5}\sin\frac{4\pi}{9}\right),$$
 * $$\left(\cos\left(\frac{j\pi}{9}\right),\,±\sin\left(\frac{j\pi}{9}\right),\,±\frac{3-\sqrt5}{2}\sin\frac{4\pi}{9},\,±\sqrt{\frac{5-\sqrt5}{2}}\sin\frac{4\pi}{9}\right),$$
 * $$\left(\cos\left(\frac{j\pi}{9}\right),\,±\sin\left(\frac{j\pi}{9}\right),\,±\left(\sqrt5-1\right)\sin\frac{4\pi}{9},\,0\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}{2},\,±\sin\frac{4\pi}{9},\,±\sqrt{5-2\sqrt5}\sin\frac{4\pi}{9}\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}{2},\,±\frac{3-\sqrt5}{2}\sin\frac{4\pi}{9},\,±\sqrt{\frac{5-\sqrt5}{2}}\sin\frac{4\pi}{9}\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}{2},\,±\left(\sqrt5-1\right)\sin\frac{4\pi}{9},\,0\right),$$