Heptagonal-truncated cubic duoprism

The heptagonal-truncated cubic duoprism or hetic is a convex uniform duoprism that consists of 7 truncated cubic prisms, 6 heptagonal-octagonal duoprisms, and 8 triangular-heptagonal duoprisms. Each vertex joins 2 truncated cubic prisms, 1 triangular-heptagonal duoprism, and 2 heptagonal-octagonal duoprisms.

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