Great enneagrammic-grand hendecagrammic duoprism

The great enneagrammic-grand hendecagrammic duoprism, also known as the 9/4-11/5 duoprism, is a uniform duoprism that consists of 11 great enneagrammic prisms and 9 grand hendecagrammic prisms, with 2 of each at each vertex.

Coordinates
The vertex coordinates of a great enneagrammic-grand hendecagrammic duoprism, centered at the origin and with edge length 4sin(4π/9)sin(5π/11), are given by: where j = 2, 4, 8 and k = 2, 4, 6, 8, 10.
 * $$\left(2\sin\frac{5\pi}{11},\,0,\,2\sin\frac{4\pi}{9},\,0\right),$$
 * $$\left(2\sin\frac{5\pi}{11},\,0,\,2\sin\frac{4\pi}{9}\cos\left(\frac{k\pi}{11}\right),\,±2\sin\frac{4\pi}{9}\sin\left(\frac{k\pi}{11}\right)\right),$$
 * $$\left(2\sin\frac{5\pi}{11}\cos\left(\frac{j\pi}{9}\right),\,±2\sin\frac{5\pi}{11}\sin\left(\frac{j\pi}{9}\right),\,2\sin\frac{4\pi}{9},\,0\right),$$
 * $$\left(2\sin\frac{5\pi}{11}\cos\left(\frac{j\pi}{9}\right),\,±2\sin\frac{5\pi}{11}\sin\left(\frac{j\pi}{9}\right),\,2\sin\frac{4\pi}{9}\cos\left(\frac{k\pi}{11}\right),\,±2\sin\frac{4\pi}{9}\sin\left(\frac{k\pi}{11}\right)\right),$$
 * $$\left(-\sin\frac{5\pi}{11},\,±\sqrt3\sin\frac{5\pi}{11},\,2\sin\frac{4\pi}{9},\,0\right),$$
 * $$\left(-\sin\frac{5\pi}{11},\,±\sqrt3\sin\frac{5\pi}{11},\,2\sin\frac{4\pi}{9}\cos\left(\frac{k\pi}{11}\right),\,±2\sin\frac{4\pi}{9}\sin\left(\frac{k\pi}{11}\right)\right),$$