Heptagonal-truncated tetrahedral duoprism

The heptagonal-truncated tetrahedral duoprism or hetut is a convex uniform duoprism that consists of 7 truncated tetrahedral prisms, 4 hexagonal-heptagonal duoprisms and 4 triangular-heptagonal duoprisms. Each vertex joins 2 truncated tetrahedral prisms, 1 triangular-heptagonal duoprism, and 2 hexagonal-heptagonal duoprisms.

Vertex coordinates
The vertices of a heptagonal-truncated tetrahedral duoprism of edge length 2sin(π/7) are given by all permutations and even sign changes of the last three coordinates of: where j = 2, 4, 6.
 * $$\left(1,\,0,\,\frac{3\sqrt2\sin\frac\pi7}2,\,\frac{\sqrt2\sin\frac\pi7}2,\,\frac{\sqrt2\sin\frac\pi7}2\right),$$
 * $$\left(\cos\left(\frac{j\pi}{7}\right),\,±\sin\left(\frac{j\pi}{7}\right),\,\frac{3\sqrt2\sin\frac\pi7}2,\,\frac{\sqrt2\sin\frac\pi7}2,\,\frac{\sqrt2\sin\frac\pi7}2\right),$$