Octagonal-decagonal duoprism

The octagonal-decagonal duoprism or odedip, also known as the 8-10 duoprism, is a uniform duoprism that consists of 8 decagonal prisms and 10 octagonal prisms, with two of each joining at each vertex.

This polychoron can be alternated into a square-pentagonal duoantiprism, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create a pentagonal-square prismantiprismoid, which is also nonuniform.

Vertex coordinates
The vertices of an octagonal-decagonal duoprism of edge length 1, centered at the origin, are given by:
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}{2},\,0,\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}{2},\,±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}{2},\,±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac12,\,0,\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac12,\,±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac12,\,±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12\right).$$

Representations
An octagonal-decagonal duoprism has the following Coxeter diagrams:


 * x8o x10o (full symmetry)
 * x5x x10o (octagons as ditetragons0
 * x5x x8o (decagons as dipentagons)
 * x4x x5x (both of these applied)