Enneagonal-icosahedral duoprism

The enneagonal-icosahedral duoprism or eike is a convex uniform duoprism that consists of 9 icosahedral prisms and 20 triangular-enneagonal duoprisms. Each vertex joins 2 icosahedral prisms and 5 triangular-enneagonal duoprisms.

Vertex coordinates
The vertices of an enneagonal-dodecahedral duoprism of edge length 2sin(π/9) are given by all even permutations of the last three coordinates of: where j = 2, 4, 8.
 * $$\left(1,\,0,\,0,\,±\sin\frac\pi9,\,±\frac{(1+\sqrt{5})\sin\frac\pi9}2\right),$$
 * $$\left(\cos\left(\frac{j\pi}9\right),\,±\sin\left(\frac{j\pi}9\right),\,0,\,±\sin\frac\pi9,\,±\frac{(1+\sqrt{5})\sin\frac\pi9}2\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}2,\,0,\,±\sin\frac\pi9,\,±\frac{(1+\sqrt{5})\sin\frac\pi9}2\right),$$