Pentagonal-grand hendecagrammic duoprism

The pentagonal-grand hendecagrammic duoprism, also known as the 5-11/5 duoprism, is a uniform duoprism that consists of 11 pentagonal prisms and 5 grand hendecagrammic prisms, with two of each at each vertex.

Vertex coordinates
The coordinates of a pentagonal-grand hendecagrammic duoprism, centered at the origin and with edge length 2sin(5π/11), are given by: where j = 2, 4, 6, 8, 10.
 * $$\left(±\sin\frac{5\pi}{11},\,-\sqrt{\frac{5+2\sqrt5}5}\sin\frac{5\pi}{11},\,1,\,0\right),$$
 * $$\left(±\sin\frac{5\pi}{11},\,-\sqrt{\frac{5+2\sqrt5}5}\sin\frac{5\pi}{11},\,\cos\left(\frac{j\pi}{11}\right),\,±\sin\left(\frac{j\pi}{11}\right)\right),$$
 * $$\left(±\frac{1+\sqrt5}2\sin\frac{5\pi}{11},\,\sqrt{\frac{5-\sqrt5}{10}}\sin\frac{5\pi}{11},\,1,\,0\right),$$
 * $$\left(±\frac{1+\sqrt5}2\sin\frac{5\pi}{11},\,\sqrt{\frac{5-\sqrt5}{10}}\sin\frac{5\pi}{11},\,\cos\left(\frac{j\pi}{11}\right),\,±\sin\left(\frac{j\pi}{11}\right)\right),$$
 * $$\left(0,\,2\sqrt{\frac{5+\sqrt5}{10}}\sin\frac{5\pi}{11},\,1,\,0\right),$$
 * $$\left(0,\,2\sqrt{\frac{5+\sqrt5}{10}}\sin\frac{5\pi}{11},\,\cos\left(\frac{j\pi}{11}\right),\,±\sin\left(\frac{j\pi}{11}\right)\right),$$