Great heptagrammic-dodecagrammic duoprism

The great heptagrammic-dodecagrammic duoprism, also known as the 7/3-12/5 duoprism, is a uniform duoprism that consists of 12 great heptagrammic prisms and 7 dodecagrammic prisms, with 2 of each at each vertex.

Vertex coordinates
The coordinates of a great heptagrammic-dodecagrammic duoprism, centered at the origin and with edge length 2sin(3π/7), are given by: where j = 2, 4, 6.
 * $$\left(1,\,0,\,±\left(\sqrt3-1\right)\sin\frac{3\pi}{7},\,±\left(\sqrt3-1\right)\sin\frac{3\pi}{7}\right),$$
 * $$\left(1,\,0,\,±\sin\frac{3\pi}{7},\,±\left(2-\sqrt3\right)\sin\frac{3\pi}{7}\right),$$
 * $$\left(1,\,0,\,±\left(2-\sqrt3\right)\sin\frac{3\pi}{7},\,±\sin\frac{3\pi}{7}\right),$$
 * $$\left(\cos\left(\frac{j\pi}{7}\right),\,±\sin\left(\frac{j\pi}{7}\right),\,±\left(\sqrt3-1\right)\sin\frac{3\pi}{7},\,±\left(\sqrt3-1\right)\sin\frac{3\pi}{7}\right),$$
 * $$\left(\cos\left(\frac{j\pi}{7}\right),\,±\sin\left(\frac{j\pi}{7}\right),\,±\sin\frac{3\pi}{7},\,±\left(2-\sqrt3\right)\sin\frac{3\pi}{7}\right),$$
 * $$\left(\cos\left(\frac{j\pi}{7}\right),\,±\sin\left(\frac{j\pi}{7}\right),\,±\left(2-\sqrt3\right)\sin\frac{3\pi}{7},\,±\sin\frac{3\pi}{7}\right),$$