Triangular-octagonal duoprism

The triangular-octagonal duoprism or todip, also known as the 3-8 duoprism, is a uniform duoprism that consists of 3 octagonal prisms, 8 triangular prisms, with 2 of each meeting at each vertex. It is also a CRF segmentochoron, being octagon atop octagonal prism. It is designated K-4.59 on Richard Klitzing's list.

Vertex coordinates
Coordinates for the vertices of a triangular-octagonal duoprism of edge length 1, centered at the origin, are given by:
 * $$\left(0,\,\frac{\sqrt3}{3},\,±\frac12,\,±\frac{1+\sqrt2}{2}\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,±\frac{1+\sqrt2}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac12,\,±\frac{1+\sqrt2}{2}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac{1+\sqrt2}{2},\,±\frac12\right).$$

Representations
A triangular-octagonal duoprism has the following Coxeter diagrams:


 * x3o x8o (full symmetry)
 * x3o x4x (A2×BC2 symmetry, octagon as ditetragon)
 * ox xx8oo&#x (octagon atop octagon prism)
 * ox xx4xx#&x (BC2×A1 axial, octagon atop octagon prism)
 * xwwx xxxx3oooo&#xt (A2×A1 axial, triangular prism-first)