Heptagonal-octahedral duoprism

The heptagonal-octahedral duoprism or heoct is a convex uniform duoprism that consists of 7 octahedral prisms and 8 triangular-heptagonal duoprisms. Each vertex joins 2 octahedral prisms and 4 triangular-heptagonal duoprisms.

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