Heptagonal-dodecahedral duoprism

The heptagonal-dodecahedral duoprism or hedoe is a convex uniform duoprism that consists of 7 dodecahedral prisms and 12 pentagonal-heptagonal duoprisms. Each vertex joins 2 dodecahedral prisms and 3 pentagonal-heptagonal duoprisms.

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