Heptagonal-cubic duoprism

The heptagonal-cubic duoprism or hecube, also known as a square-heptagonal duoprismatic prism, is a convex uniform duoprism that consists of 7 tesseracts and 6 square-heptagonal duoprisms. Each vertex joins 2 tesseracts and 3 square-heptagonal duoprisms. It is a duoprism based on a square and a heptagonal prism, which makes it a convex segmentoteron.

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

Representations
A heptagonal-cubic duoprism has the following Coxeter diagrams:
 * x7o x4o3o (full symmetry)
 * x x4o x7o (square-heptagonal duoprismatic prism)
 * x x x x7o (heptagonal prismatic prismatic prism)