Pentagonal-great heptagrammic duoprism

The pentagonal-great heptagrammic duoprism, also known as pagishdip or the 5-7/3 duoprism, is a uniform duoprism that consists of 7 pentagonal prisms and 5 great heptagrammic prisms, with two of each at each vertex.

Vertex coordinates
The coordinates of a pentagonal-great heptagrammic duoprism, centered at the origin and with edge length 2sin(3π/7), are given by: where j = 2, 4, 6.
 * $$\left(±\sin\frac{3\pi}7,\,-\sqrt{\frac{5+2\sqrt5}5}\sin\frac{3\pi}7,\,1,\,0\right),$$
 * $$\left(±\sin\frac{3\pi}7,\,-\sqrt{\frac{5+2\sqrt5}5}\sin\frac{3\pi}7,\,\cos\left(\frac{j\pi}7\right),\,±\sin\left(\frac{j\pi}7\right)\right),$$
 * $$\left(±\frac{1+\sqrt5}2\sin\frac{3\pi}7,\,\sqrt{\frac{5-\sqrt5}{10}}\sin\frac{3\pi}7,\,1,\,0\right),$$
 * $$\left(±\frac{1+\sqrt5}2\sin\frac{3\pi}7,\,\sqrt{\frac{5-\sqrt5}{10}}\sin\frac{3\pi}7,\,\cos\left(\frac{j\pi}7\right),\,±\sin\left(\frac{j\pi}7\right)\right),$$
 * $$\left(0,\,2\sqrt{\frac{5+\sqrt5}{10}}\sin\frac{3\pi}7,\,1,\,0\right),$$
 * $$\left(0,\,2\sqrt{\frac{5+\sqrt5}{10}}\sin\frac{3\pi}7,\,\cos\left(\frac{j\pi}7\right),\,±\sin\left(\frac{j\pi}7\right)\right),$$