Heptagonal-truncated dodecahedral duoprism

The heptagonal-truncated dodecahedral duoprism or hetid is a convex uniform duoprism that consists of 7 truncated dodecahedral prisms, 12 heptagonal-decagonal duoprisms, and 20 triangular-heptagonal duoprisms. Each vertex joins 2 truncated dodecahedral prisms, 1 triangular-heptagonal duoprism, and 2 heptagonal-decagonal duoprisms.

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