Enneagonal-snub dodecahedral duoprism

The enneagonal-snub dodecahedral duoprism or esnid is a convex uniform duoprism that consists of 9 snub dodecahedral prisms, 12 pentagonal-enneagonal duoprisms and 80 triangular-enneagonal duoprisms of two kinds. Each vertex joins 2 snub dodecahedral prisms, 4 triangular-enneagonal duoprisms, and 1 pentagonal-enneagonal duoprism.

Vertex coordinates
The vertices of an enneagonal-snub dodecahedral duoprism of edge length 2sin(π/9) are given by all even permutations with an odd number of sign changes of the last three coordinates of: as well as all even permutations with an even number of sign changes of the last three coordinates of: where
 * $$\left(1,\,0,\,\phi\sqrt{\phi\left(\xi-1-\frac1\xi\right)}\sin\frac\pi9,\,\xi\phi\sqrt{3-\xi^2}\sin\frac\pi9,\,\phi\sqrt{\xi(\xi+\phi)+1}\sin\frac\pi9\right),$$
 * $$\left(\cos\frac{j\pi}9,\,±\sin\frac{j\pi}9,\,\phi\sqrt{\phi\left(\xi-1-\frac1\xi\right)}\sin\frac\pi9,\,\xi\phi\sqrt{3-\xi^2}\sin\frac\pi9,\,\phi\sqrt{\xi(\xi+\phi)+1}\sin\frac\pi9\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}2,\,\phi\sqrt{\phi\left(\xi-1-\frac1\xi\right)}\sin\frac\pi9,\,\xi\phi\sqrt{3-\xi^2}\sin\frac\pi9,\,\phi\sqrt{\xi(\xi+\phi)+1}\sin\frac\pi9\right),$$
 * $$\left(1,\,0,\,\phi\sqrt{3-\xi^2}\sin\frac\pi9,\,\xi\phi\sqrt{1-\xi+\frac{1+\phi}\xi}\sin\frac\pi9,\,\phi\sqrt{\xi(\xi+1)}\sin\frac\pi9\right),$$
 * $$\left(\cos\frac{j\pi}9,\,±\sin\frac{j\pi}9,\,\phi\sqrt{3-\xi^2}\sin\frac\pi9,\,\xi\phi\sqrt{1-\xi+\frac{1+\phi}\xi}\sin\frac\pi9,\,\phi\sqrt{\xi(\xi+1)}\sin\frac\pi9\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}2,\,\phi\sqrt{3-\xi^2}\sin\frac\pi9,\,\xi\phi\sqrt{1-\xi+\frac{1+\phi}\xi}\sin\frac\pi9,\,\phi\sqrt{\xi(\xi+1)}\sin\frac\pi9\right),$$
 * $$\left(1,\,0,\,\xi^2\phi\sqrt{\phi\left(\xi-1-\frac1\xi\right)}\sin\frac\pi9,\,\phi\sqrt{\xi+1-\phi}\sin\frac\pi9,\,\sqrt{\xi^2(1+2\phi)-\phi}\sin\frac\pi9\right),$$
 * $$\left(\cos\frac{j\pi}9,\,±\sin\frac{j\pi}9,\,\xi^2\phi\sqrt{\phi\left(\xi-1-\frac1\xi\right)}\sin\frac\pi9,\,\phi\sqrt{\xi+1-\phi}\sin\frac\pi9,\,\sqrt{\xi^2(1+2\phi)-\phi}\sin\frac\pi9\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}2,\,\xi^2\phi\sqrt{\phi\left(\xi-1-\frac1\xi\right)}\sin\frac\pi9,\,\phi\sqrt{\xi+1-\phi}\sin\frac\pi9,\,\sqrt{\xi^2(1+2\phi)-\phi}\sin\frac\pi9\right),$$
 * $$\left(1,\,0,\,\xi^2\phi\sqrt{3-\xi^2}\sin\frac\pi9,\,\xi\phi\sqrt{\phi(\xi-1-\frac1\xi)}\sin\frac\pi9,\,\frac{\phi^2\sqrt{\xi(\xi+\phi)+1}\sin\frac\pi9}\xi\right),$$
 * $$\left(\cos\frac{j\pi}9,\,±\sin\frac{j\pi}9,\,\xi^2\phi\sqrt{3-\xi^2}\sin\frac\pi9,\,\xi\phi\sqrt{\phi(\xi-1-\frac1\xi)}\sin\frac\pi9,\,\frac{\phi^2\sqrt{\xi(\xi+\phi)+1}\sin\frac\pi9}\xi\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}2,\,\xi^2\phi\sqrt{3-\xi^2}\sin\frac\pi9,\,\xi\phi\sqrt{\phi(\xi-1-\frac1\xi)}\sin\frac\pi9,\,\frac{\phi^2\sqrt{\xi(\xi+\phi)+1}\sin\frac\pi9}\xi\right),$$
 * $$\left(1,\,0,\,\sqrt{\phi(\xi+2)+2}\sin\frac\pi9,\,\phi\sqrt{1-\xi+\frac{1+\phi}\xi}\sin\frac\pi9,\,\xi\sqrt{\xi(1+\phi)-\phi}\sin\frac\pi9\right),$$
 * $$\left(\cos\frac{j\pi}9,\,±\sin\frac{j\pi}9,\,\sqrt{\phi(\xi+2)+2}\sin\frac\pi9,\,\phi\sqrt{1-\xi+\frac{1+\phi}\xi}\sin\frac\pi9,\,\xi\sqrt{\xi(1+\phi)-\phi}\sin\frac\pi9\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}2,\,\sqrt{\phi(\xi+2)+2}\sin\frac\pi9,\,\phi\sqrt{1-\xi+\frac{1+\phi}\xi}\sin\frac\pi9,\,\xi\sqrt{\xi(1+\phi)-\phi}\sin\frac\pi9\right),$$
 * j = 2, 4, 8,
 * $$\phi = \frac{1+\sqrt5}2,$$
 * $$\xi = \sqrt[3]{\frac{\phi+\sqrt{\phi-\frac5{27}}}2}+\sqrt[3]{\frac{\phi-\sqrt{\phi-\frac5{27}}}2}.$$