Pentagrammic-heptagonal duoprism

The pentagrammic-heptagonal duoprism, also known as stahedip or the 5/2-7 duoprism, is a uniform duoprism that consists of 7 pentagrammic prisms and 5 heptagonal prisms, with 2 of each at each vertex.

Vertex coordinates
The coordinates of a pentagrammic-heptagonal duoprism, centered at the origin and with edge length 2sin(π/7), are given by: where j = 2, 4, 6.
 * $$\left(±\sin\frac{\pi}7,\,-\sqrt{\frac{5-2\sqrt5}5}\sin\frac{\pi}7,\,1,\,0\right),$$
 * $$\left(±\sin\frac{\pi}7,\,-\sqrt{\frac{5-2\sqrt5}5}\sin\frac{\pi}7,\,\cos\left(\frac{j\pi}7\right),\,±\sin\left(\frac{j\pi}7\right)\right),$$
 * $$\left(±\frac{\sqrt5-1}2\sin\frac{\pi}7,\,\sqrt{\frac{5+\sqrt5}{10}}\sin\frac{\pi}7,\,1,\,0\right),$$
 * $$\left(±\frac{\sqrt5-1}2\sin\frac{\pi}7,\,\sqrt{\frac{5+\sqrt5}{10}}\sin\frac{\pi}7,\,\cos\left(\frac{j\pi}7\right),\,±\sin\left(\frac{j\pi}7\right)\right),$$
 * $$\left(0,\,-2\sqrt{\frac{5-\sqrt5}{10}}\sin\frac{\pi}7,\,1,\,0\right),$$
 * $$\left(0,\,-2\sqrt{\frac{5-\sqrt5}{10}}\sin\frac{\pi}7,\,\cos\left(\frac{j\pi}7\right),\,±\sin\left(\frac{j\pi}7\right)\right),$$