Heptagonal-great rhombicuboctahedral duoprism

The heptagonal-great rhombicuboctahedral duoprism or hegirco is a convex uniform duoprism that consists of 7 great rhombicuboctahedral prisms, 6 heptagonal-octagonal duoprisms, 8 hexagonal-heptagonal duoprisms, and 12 square-heptagonal duoprisms. Each vertex joins 2 great rhombicuboctahedral prisms, 1 square-heptagonal duoprism, 1 hexagonal-heptagonal duoprism, and 1 heptagonal-octagonal duoprism.

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