Heptagonal-small rhombicuboctahedral duoprism

The heptagonal-small rhombicuboctahedral duoprism or hesirco is a convex uniform duoprism that consists of 7 small rhombicuboctahedral prisms, 18 square-heptagonal duoprisms of two kinds, and 8 triangular-heptagonal duoprisms. Each vertex joins 2 small rhombicuboctahedral prisms, 1 triangular-heptagonal duoprism, and 3 square-heptagonal duoprisms.

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