Heptagonal-great rhombicosidodecahedral duoprism

The heptagonal-great rhombicosidodecahedral duoprism or hegrid is a convex uniform duoprism that consists of 7 great rhombicosidodecahedral prisms, 12 heptagonal-decagonal duoprisms, 20 hexagonal-heptagonal duoprisms and 30 square-heptagonal duoprisms. Each vertex joins 2 great rhombicosidodecahedral prisms, 1 square-heptagonal duoprism, 1 hexagonal-heptagonal duoprism, and 1 heptagonal-decagonal duoprism.

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