Heptagonal-cuboctahedral duoprism

The heptagonal-cuboctahedral duoprism or heco is a convex uniform duoprism that consists of 7 cuboctahedral prisms, 6 square-heptagonal duoprisms and 8 triangular-heptagonal duoprisms. Each vertex joins 2 cuboctahedral prisms, 2 triangular-heptagonal duoprisms, and 2 square-heptagonal duoprisms.

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