Enneagonal-icosidodecahedral duoprism

The enneagonal-icosidodecahedral duoprism or eid is a convex uniform duoprism that consists of 9 icosidodecahedral prisms, 12 pentagonal-enneagonal duoprisms and 20 triangular-enneagonal duoprisms. Each vertex joins 2 icosidodecahedral prisms, 2 triangular-enneagonal duoprisms, and 2 pentagonal-enneagonal duoprisms.

Vertex coordinates
The vertices of an enneagonal-icosidodecahedral 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.
 * $$\left(1,\,0,\,0,\,0,\,±(1+\sqrt5)\sin\frac\pi9\right),$$
 * $$\left(\cos\left(\frac{j\pi}9\right),\,±\sin\left(\frac{j\pi}9\right),\,0,\,0,\,±(1+\sqrt5)\sin\frac\pi9\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}2,\,0,\,0,\,±(1+\sqrt5)\sin\frac\pi9\right),$$
 * $$\left(1,\,0,\,±\sin\frac\pi9,\,±\frac{(1+\sqrt5)\sin\frac\pi9}2,\,±\frac{(3+\sqrt5)\sin\frac\pi9}2\right),$$
 * $$\left(\cos\left(\frac{j\pi}9\right),\,±\sin\left(\frac{j\pi}9\right),\,±\sin\frac\pi9,\,±\frac{(1+\sqrt5)\sin\frac\pi9}2,\,±\frac{(3+\sqrt5)\sin\frac\pi9}2\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}2,\,±\sin\frac\pi9,\,±\frac{(1+\sqrt5)\sin\frac\pi9}2,\,±\frac{(3+\sqrt5)\sin\frac\pi9}2\right),$$