Enneagonal-small rhombicosidodecahedral duoprism

The enneagonal-small rhombicosidodecahedral duoprism or esrid is a convex uniform duoprism that consists of 9 small rhombicosidodecahedral prisms, 12 pentagonal-enneagonal duoprisms, 30 square-enneagonal duoprisms, and 20 triangular-enneagonal duoprisms. Each vertex joins 2 small rhombicosidodecahedral prisms, 1 triangular-enneagonal duoprism, 2 square-enneagonal duoprisms, and 1 pentagonal-enneagonal duoprism.

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