Enneagonal-small rhombicuboctahedral duoprism

The enneagonal-small rhombicuboctahedral duoprism or esirco is a convex uniform duoprism that consists of 9 small rhombicuboctahedral prisms, 18 square-enneagonal duoprisms of two kinds, and 8 triangular-enneagonal duoprisms. Each vertex joins 2 small rhombicuboctahedral prisms, 1 triangular-enneagonal duoprism, and 3 square-enneagonal duoprisms.

Vertex coordinates
The vertices of an enneagonal-small rhombicuboctahedral duoprism of edge length 2sin(π/9) are given by all permutations of the last three coordinates of: where j = 2, 4, 8.
 * $$\left(1,\,0,\,±\sin\frac\pi9,\,±\sin\frac\pi9,\,±(1+\sqrt2)\sin\frac\pi9\right),$$
 * $$\left(\cos\left(\frac{j\pi}9\right),\,±\sin\left(\frac{j\pi}9\right),\,±\sin\frac\pi9,\,±\sin\frac\pi9,\,±(1+\sqrt2)\sin\frac\pi9\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}2,\,±\sin\frac\pi9,\,±\sin\frac\pi9,\,±(1+\sqrt2)\sin\frac\pi9\right),$$