Enneagonal-truncated tetrahedral duoprism

The enneagonal-truncated tetrahedral duoprism or etut is a convex uniform duoprism that consists of 9 truncated tetrahedral prisms, 4 hexagonal-enneagonal duoprisms and 4 triangular-enneagonal duoprisms. Each vertex joins 2 truncated tetrahedral prisms, 1 triangular-enneagonal duoprism, and 2 hexagonal-enneagonal duoprisms.

Vertex coordinates
The vertices of an enneagonal-truncated tetrahedral duoprism of edge length 2sin(π/9) are given by all permutations and even sign changes of the last three coordinates of: where j = 2, 4, 8.
 * $$\left(1,\,0,\,\frac{3\sqrt2\sin\frac\pi9}2,\,\frac{\sqrt2\sin\frac\pi9}2,\,\frac{\sqrt2\sin\frac\pi9}2\right),$$
 * $$\left(\cos\left(\frac{j\pi}9\right),\,±\sin\left(\frac{j\pi}9\right),\,\frac{3\sqrt2\sin\frac\pi9}2,\,\frac{\sqrt2\sin\frac\pi9}2,\,\frac{\sqrt2\sin\frac\pi9}2\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}2,\,\frac{3\sqrt2\sin\frac\pi9}2,\,\frac{\sqrt2\sin\frac\pi9}2,\,\frac{\sqrt2\sin\frac\pi9}2\right),$$