Great heptagrammic-decagrammic duoprism

The great heptagrammic-decagrammic duoprism, also known as gishstadedip or the 7/3-10/3 duoprism, is a uniform duoprism that consists of 10 great heptagrammic prisms and 7 decagrammic prisms, with 2 of each at each vertex.

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