Heptagonal-icosidodecahedral duoprism

The heptagonal-icosidodecahedral duoprism or heid is a convex uniform duoprism that consists of 7 icosidodecahedral prisms, 12 pentagonal-heptagonal duoprisms, and 20 triangular-heptagonal duoprisms. Each vertex joins 2 icosidodecahedral prisms, 2 triangular-heptagonal duoprisms, and 2 pentagonal-heptagonal duoprisms.

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