Triangular-heptagonal duoprismatic prism

The triangular-heptagonal duoprismatic prism or trahep, also known as the triangular-heptagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 triangular-heptagonal duoprisms, 3 square-heptagonal duoprisms, and 7 triangular-square duoprisms. Each vertex joins 2 triangular-square duoprisms, 2 square-heptagonal duoprisms, and 1 triangular-heptagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

Vertex coordinates
The vertices of a triangular-heptagonal duoprismatic prism of edge length 2sin(π/7) are given by: where j = 2, 4, 6.
 * $$\left(0,\,\frac{2\sqrt3\sin\frac\pi7}3,\,1,\,0,\,±\sin\frac\pi7\right),$$
 * $$\left(±\sin\frac\pi7,\,-\frac{\sqrt3\sin\frac\pi7}3,\,1,\,0,\,±\sin\frac\pi7\right),$$
 * $$\left(0,\,\frac{2\sqrt3\sin\frac\pi7}3,\,\cos\frac{j\pi}7,\,±\sin\frac{j\pi}7,\,±\sin\frac\pi7\right),$$
 * $$\left(±\sin\frac\pi7,\,-\frac{\sqrt3\sin\frac\pi7}3,\,\cos\frac{j\pi}7,\,±\sin\frac{j\pi}7,\,±\sin\frac\pi7\right).$$

Representations
A triangular-heptagonal duoprismatic prism has the following Coxeter diagrams:
 * x x3o x7o (full symmetry)
 * xx3oo xx7oo&#x (triangular-heptagonal duoprism atop triangular-heptagonal duoprism)
 * ox xx xx7oo&#x (heptagonal prism atop square-heptagonal duoprism)