Pentagonal-heptagonal duoprism

The pentagonal-heptagonal duoprism or pheddip, also known as the 5-7 duoprism, is a uniform duoprism that consists of 5 heptagonal prisms and 7 pentagonal prisms, with two of each joining at each vertex.

Vertex coordinates
The coordinates of a pentagonal-heptagonal duoprism, centered at the origin and with edge length 2sin(π/7), are given by: where j = 2, 4, 6.
 * $$\left(±\sin\frac\pi7,-\sqrt{\frac{5+2\sqrt5}5}\sin\frac\pi7,1,0\right),$$
 * $$\left(±\sin\frac\pi7,-\sqrt{\frac{5+2\sqrt5}5}\sin\frac\pi7,\cos\left(\frac{j\pi}7\right),±\sin\left(\frac{j\pi}7\right)\right),$$
 * $$\left(±\frac{1+\sqrt5}2\sin\frac\pi7,\sqrt{\frac{5-\sqrt5}{10}}\sin\frac\pi7,1,0\right),$$
 * $$\left(±\frac{1+\sqrt5}2\sin\frac\pi7,\sqrt{\frac{5-\sqrt5}{10}}\sin\frac\pi7,\cos\left(\frac{j\pi}7\right),±\sin\left(\frac{j\pi}7\right)\right),$$
 * $$\left(0,2\sqrt{\frac{5+\sqrt5}{10}}\sin\frac\pi7,1,0\right),$$
 * $$\left(0,2\sqrt{\frac{5+\sqrt5}{10}}\sin\frac\pi7,\cos\left(\frac{j\pi}7\right),±\sin\left(\frac{j\pi}7\right)\right),$$