Heptagonal-icosahedral duoprism

The heptagonal-icosahedral duoprism or heike is a convex uniform duoprism that consists of 7 icosahedral prisms and 20 triangular-heptagonal duoprisms. Each vertex joins 2 icosahedral prisms and 5 triangular-heptagonal duoprisms.

Vertex coordinates
The vertices of a heptagonal-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.
 * $$\left(1,\,0,\,0,\,±\sin\frac\pi7,\,±\frac{(1+\sqrt{5})\sin\frac\pi7}2\right),$$
 * $$\left(\cos\left(\frac{j\pi}{7}\right),\,±\sin\left(\frac{j\pi}{7}\right),\,0,\,±\sin\frac\pi7,\,±\frac{(1+\sqrt{5})\sin\frac\pi7}2\right),$$