Octagonal-dodecagonal duoprismatic prism

The octagonal-dodecagonal duoprismatic prism or otwip, also known as the octagonal-dodecagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 octagonal-dodecagonal duoprisms, 8 square-dodecagonal duoprisms, and 12 square-octagonal duoprisms. Each vertex joins 2 square-octagonal duoprisms, 2 square-dodecagonal duoprisms, and 1 octagonal-dodecagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

This polyteron can be alternated into a square-hexagonal duoantiprismatic antiprism, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create a hexagonal-square prismatic prismantiprismoid or the dodecagons into long ditrigons to create a square-hexagonal prismatic prismantiprismoid, which are also both nonuniform.

Vertex coordinates
The vertices of an octagonal-dodecagonal duoprismatic prism of edge length 1 are given by all permutations of the first two coordinates of:
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}2,\,±\frac{1+\sqrt3}2,\,±\frac{1+\sqrt3}2,\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}2,\,±\frac12,\,±\frac{2+\sqrt3}2,\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}2,\,±\frac{2+\sqrt3}2,\,±\frac12,\,±\frac12\right).$$

Representations
An octagonal-dodecagonal duoprismatic prism has the following Coxeter diagrams:
 * x x8o x12o (full symmetry)
 * x x4x x12o (octagons as ditetragons)
 * x x8o x6x (dodecagons as dihexagons)
 * x x4x x6x
 * xx8oo xx12oo&#x (octagonal-enneagonal duoprism atop octagonal-enneagonal duoprism)
 * xx4xx xx12oo&#x
 * xx8oo xx6xx&#x
 * xx4xx xx6xx&#x