Octagonal-dodecagonal duoprism

The octagonal-dodecagonal duoprism or otwadip, also known as the 8-12 duoprism, is a uniform duoprism that consists of 8 dodecagonal prisms and 12 octagonal prisms, with two of each joining at each vertex.

This polychoron can be alternated into a square-hexagonal duoantiprism, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create a hexagonal-square prismantiprismoid or the dodecagons into long ditrigons to create a square-hexagonal prismantiprismoid, or it can be subsymmetrically faceted into a digonal-triangular tetraswirlprism, which are nonuniform.

Vertex coordinates
The coordinates of an octagonal-dodecagonal duoprism of edge length 1, centered at the origin, are given by:
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}{2},\,±\frac12,\,±\frac{2+\sqrt3}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}{2},\,±\frac{2+\sqrt3}{2},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac12,\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2}\right),$$
 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac12,\,±\frac12,\,±\frac{2+\sqrt3}{2}\right),$$
 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac12\right).$$

Representations
An octagonal-dodecagonal duoprism has the fllowing Coxeter diagrams:


 * x8o x12o (full symmetry)
 * x4x x12o (octagons as ditetragons)
 * x6x x8o (dodecagons as dihexagons)
 * x4x x6x (both of these applied)