Heptagonal-tetrahedral duoprism

The heptagonal-tetrahedral duoprism or hetet is a convex uniform duoprism that consists of 7 tetrahedral prisms and 4 triangular-heptagonal duoprisms. Each vertex joins 2 tetrahedral prisms and 3 triangular-heptagonal duoprisms.

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