Heptagonal-small rhombicosidodecahedral duoprism

The heptagonal-small rhombicosidodecahedral duoprism or hesrid is a convex uniform duoprism that consists of 7 small rhombicosidodecahedral prisms, 12 pentagonal-heptagonal duoprisms, 30 square-heptagonal duoprisms, and 20 triangular-heptagonal duoprisms. Each vertex joins 2 small rhombicosidodecahedral prisms, 1 triangular-heptagonal duoprism, 2 square-heptagonal duoprisms, and 1 pentagonal-heptagonal duoprism.

Vertex coordinates
The vertices of a heptagonal-small rhombicosidodecahedral 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.
 * $$\left(1,\,0,\,±\sin\frac\pi7,\,±\sin\frac\pi7,\,±(2+\sqrt5)\sin\frac\pi7\right),$$
 * $$\left(\cos\left(\frac{j\pi}7\right),\,±\sin\left(\frac{j\pi}7\right),\,±\sin\frac\pi7,\,±\sin\frac\pi7,\,±(2+\sqrt5)\sin\frac\pi7\right),$$
 * $$\left(1,\,0,\,0,\,±\frac{(3+\sqrt5)\sin\frac\pi7}2,\,±\frac{(5+\sqrt5)\sin\frac\pi7}2\right),$$
 * $$\left(\cos\left(\frac{j\pi}7\right),\,±\sin\left(\frac{j\pi}7\right),\,0,\,±\frac{(3+\sqrt5)\sin\frac\pi7}2,\,±\frac{(5+\sqrt5)\sin\frac\pi7}2\right),$$
 * $$\left(1,\,0,\,±\frac{(1+\sqrt5)\sin\frac\pi7}2,\,±(1+\sqrt5)\sin\frac\pi7,\,±\frac{(3+\sqrt5)\sin\frac\pi7}2\right),$$
 * $$\left(\cos\left(\frac{j\pi}7\right),\,±\sin\left(\frac{j\pi}7\right),\,±\frac{(1+\sqrt5)\sin\frac\pi7}2,\,±(1+\sqrt5)\sin\frac\pi7,\,±\frac{(3+\sqrt5)\sin\frac\pi7}2\right),$$