Triangular-enneagonal duoprismatic prism

The triangular-enneagonal duoprismatic prism or trep, also known as the triangular-enneagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 triangular-enneagonal duoprisms, 3 square-enneagonal duoprisms, and 9 triangular-square duoprisms. Each vertex joins 2 triangular-square duoprisms, 2 square-enneagonal duoprisms, and 1 triangular-enneagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

Vertex coordinates
The vertices of a triangular-enneagonal duoprismatic prism of edge length 2sin(π/9) are given by: where j = 2, 4, 8.
 * $$\left(0,\,\frac{2\sqrt3\sin\frac\pi9}3,\,1,\,0,\,±\sin\frac\pi9\right),$$
 * $$\left(±\sin\frac\pi9,\,-\frac{\sqrt3\sin\frac\pi9}3,\,1,\,0,\,±\sin\frac\pi9\right),$$
 * $$\left(0,\,\frac{2\sqrt3\sin\frac\pi9}3,\,\cos\frac{j\pi}9,\,±\sin\frac{j\pi}9,\,±\sin\frac\pi9\right),$$
 * $$\left(±\sin\frac\pi9,\,-\frac{\sqrt3\sin\frac\pi9}3,\,\cos\frac{j\pi}9,\,±\sin\frac{j\pi}9,\,±\sin\frac\pi9\right),$$
 * $$\left(0,\,\frac{2\sqrt3\sin\frac\pi9}3,\,-\frac12,\,±\frac{\sqrt3}2,\,±\sin\frac\pi9\right),$$
 * $$\left(±\sin\frac\pi9,\,-\frac{\sqrt3\sin\frac\pi9}3,\,-\frac12,\,±\frac{\sqrt3}2,\,±\sin\frac\pi9\right).$$

Representations
A triangular-enneagonal duoprismatic prism has the following Coxeter diagrams:
 * x x3o x9o (full symmetry)
 * xx3oo xx9oo&#x (triangular-enneagonal duoprism atop triangular-enneagonal duoprism)
 * ox xx xx9oo&#x (enneagonal prism atop square-enneagonal duoprism)