Heptagonal-truncated icosahedral duoprism

The heptagonal-truncated icosahedral duoprism or heti is a convex uniform duoprism that consists of 7 truncated icosahedral prisms, 20 hexagonal-heptagonal duoprisms and 12 pentagonal-heptagonal duoprisms. Each vertex joins 2 truncated icosahedral prisms, 1 pentagonal-heptagonal duoprism, and 2 hexagonal-heptagonal duoprisms.

Vertex coordinates
The vertices of a heptagonal-truncated icosahedral duoprism of edge length 2sin(π/7) are given by all even permutations of the last three coordinates of: where j = 2, 4, 6.
 * $$\left(1,\,0,\,0,\,±\sin\frac\pi7,\,±3\frac{(1+\sqrt5)\sin\frac\pi7}2\right),$$
 * $$\left(1,\,0,\,±\sin\frac\pi7,\,±\frac{(5+\sqrt5)\sin\frac\pi7}2,\,±(1+\sqrt5)\sin\frac\pi7\right),$$
 * $$\left(1,\,0,\,±\frac{(1+\sqrt5)\sin\frac\pi7}2,\,±2\sin\frac\pi7,\,±(2+\sqrt5)\sin\frac\pi7\right),$$
 * $$\left(\cos\left(\frac{j\pi}7\right),\,±\sin\left(\frac{j\pi}7\right),\,0,\,±\sin\frac\pi7,\,±3\frac{(1+\sqrt5)\sin\frac\pi7}2\right),$$
 * $$\left(\cos\left(\frac{j\pi}7\right),\,±\sin\left(\frac{j\pi}7\right),\,±\sin\frac\pi7,\,±\frac{(5+\sqrt5)\sin\frac\pi7}2,\,±(1+\sqrt5)\sin\frac\pi7\right),$$
 * $$\left(\cos\left(\frac{j\pi}7\right),\,±\sin\left(\frac{j\pi}7\right),\,±\frac{(1+\sqrt5)\sin\frac\pi7}2,\,±2\sin\frac\pi7,\,±(2+\sqrt5)\sin\frac\pi7\right),$$