Heptagonal-dodecagrammic duoprism

The heptagonal-dodecagrammic duoprism, also known as the 7-12/5 duoprism, is a uniform duoprism that consists of 12 heptagonal prisms and 7 dodecagrammic prisms, with 2 of each at each vertex.

Vertex coordinates
The coordinates of a heptagonal-dodecagrammic duoprism, centered at the origin and with edge length 2sin(π/7), are given by: where j = 2, 4, 6.
 * $$\left(1,\,0,\,±\left(\sqrt3-1\right)\sin\frac{\pi}7,\,±\left(\sqrt3-1\right)\sin\frac{\pi}7\right),$$
 * $$\left(1,\,0,\,±\sin\frac{\pi}7,\,±\left(2-\sqrt3\right)\sin\frac{\pi}7\right),$$
 * $$\left(1,\,0,\,±\left(2-\sqrt3\right)\sin\frac{\pi}7,\,±\sin\frac{\pi}7\right),$$
 * $$\left(\cos\left(\frac{j\pi}7\right),\,±\sin\left(\frac{j\pi}7\right),\,±\left(\sqrt3-1\right)\sin\frac{\pi}7,\,±\left(\sqrt3-1\right)\sin\frac{\pi}7\right),$$
 * $$\left(\cos\left(\frac{j\pi}7\right),\,±\sin\left(\frac{j\pi}7\right),\,±\sin\frac{\pi}7,\,±\left(2-\sqrt3\right)\sin\frac{\pi}7\right),$$
 * $$\left(\cos\left(\frac{j\pi}7\right),\,±\sin\left(\frac{j\pi}7\right),\,±\left(2-\sqrt3\right)\sin\frac{\pi}7,\,±\sin\frac{\pi}7\right),$$