Triangular-octagonal duoprismatic prism

The triangular-octagonal duoprismatic prism or trop, also known as the triangular-octagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 triangular-octagonal duoprisms, 3 square-octagonal duoprisms, and 8 triangular-square duoprisms. Each vertex joins 2 triangular-square duoprisms, 2 square-octagonal duoprisms, and 1 triangular-octagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

Vertex coordinates
The vertices of a triangular-octagonal duoprismatic prism of edge length 1 are given by all permutations of the third and fourth coordinates of:
 * $$\left(0,\,\frac{\sqrt3}3,\,±\frac12,\,±\frac{1+\sqrt2}2,\,±\frac12\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}6,\,±\frac12,\,±\frac{1+\sqrt2}2,\,±\frac12\right).$$

Representations
A triangular-octagonal duoprismatic prism has the following Coxeter diagrams:
 * x x3o x8o (full symmetry)
 * xx3oo xx8oo&#x (triangular-octagonal duoprism atop triangular-octagonal duoprism)
 * ox xx xx8oo&#x (octagonal prism atop square-octagonal duoprism)