Enneagonal-great rhombicosidodecahedral duoprism

The enneagonal-great rhombicosidodecahedral duoprism or egrid is a convex uniform duoprism that consists of 9 great rhombicosidodecahedral prisms, 12 enneagonal-decagonal duoprisms, 20 hexagonal-enneagonal duoprisms, and 30 square-enneagonal duoprisms. Each vertex joins 2 great rhombicosidodecahedral prisms, 1 square-enneagonal duoprism, 1 hexagonal-enneagonal duoprism, and 1 enneagonal-decagonal duoprism.

Vertex coordinates
The vertices of an enneagonal-great rhombicosidodecahedral duoprism of edge length 2sin(π/9) 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, 8.
 * $$\left(1,\,0,\,±\sin\frac\pi9,\,±\sin\frac\pi9,\,(3+2\sqrt5)\sin\frac\pi9\right),$$
 * $$\left(\cos\left(\frac{j\pi}9\right),\,±\sin\left(\frac{j\pi}9\right),\,±\sin\frac\pi9,\,±\sin\frac\pi9,\,(3+2\sqrt5)\sin\frac\pi9\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}2,\,±\sin\frac\pi9,\,±\sin\frac\pi9,\,(3+2\sqrt5)\sin\frac\pi9\right),$$
 * $$\left(1,\,0,\,±\sin\frac\pi9,\,±(2+\sqrt5)\sin\frac\pi9,\,±(4+\sqrt5)\sin\frac\pi9\right),$$
 * $$\left(\cos\left(\frac{j\pi}9\right),\,±\sin\left(\frac{j\pi}9\right),\,±\sin\frac\pi9,\,±(2+\sqrt5)\sin\frac\pi9,\,±(4+\sqrt5)\sin\frac\pi9\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}2,\,±\sin\frac\pi9,\,±(2+\sqrt5)\sin\frac\pi9,\,±(4+\sqrt5)\sin\frac\pi9\right),$$
 * $$\left(1,\,0,\,±2\sin\frac\pi9,\,±\frac{(3+\sqrt5)\sin\frac\pi9}2,\,±\frac{(7+3\sqrt5)\sin\frac\pi9}2\right),$$
 * $$\left(\cos\left(\frac{j\pi}9\right),\,±\sin\left(\frac{j\pi}9\right),\,±2\sin\frac\pi9,\,±\frac{(3+\sqrt5)\sin\frac\pi9}2,\,±\frac{(7+3\sqrt5)\sin\frac\pi9}2\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}2,\,±2\sin\frac\pi9,\,±\frac{(3+\sqrt5)\sin\frac\pi9}2,\,±\frac{(7+3\sqrt5)\sin\frac\pi9}2\right),$$
 * $$\left(1,\,0,\,±\frac{(3+\sqrt5)\sin\frac\pi9}2,\,±3\frac{(1+\sqrt5)\sin\frac\pi9}2,\,±(3+\sqrt5)\sin\frac\pi9\right),$$
 * $$\left(\cos\left(\frac{j\pi}9\right),\,±\sin\left(\frac{j\pi}9\right),\,±\frac{(3+\sqrt5)\sin\frac\pi9}2,\,±3\frac{(1+\sqrt5)\sin\frac\pi9}2,\,±(3+\sqrt5)\sin\frac\pi9\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}2,\,±\frac{(3+\sqrt5)\sin\frac\pi9}2,\,±3\frac{(1+\sqrt5)\sin\frac\pi9}2,\,±(3+\sqrt5)\sin\frac\pi9\right),$$
 * $$\left(1,\,0,\,±(1+\sqrt5)\sin\frac\pi9,\,±\frac{(5+3\sqrt5)\sin\frac\pi9}2,\,±\frac{(5+\sqrt5)\sin\frac\pi9}2\right),$$
 * $$\left(\cos\left(\frac{j\pi}9\right),\,±\sin\left(\frac{j\pi}9\right),\,±(1+\sqrt5)\sin\frac\pi9,\,±\frac{(5+3\sqrt5)\sin\frac\pi9}2,\,±\frac{(5+\sqrt5)\sin\frac\pi9}2\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}2,\,±(1+\sqrt5)\sin\frac\pi9,\,±\frac{(5+3\sqrt5)\sin\frac\pi9}2,\,±\frac{(5+\sqrt5)\sin\frac\pi9}2\right),$$