Dodecagonal duoprismatic prism

The dodecagonal duoprismatic prism or twatwip, also known as the dodecagonal-dodecagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 dodecagonal duoprisms and 24 square-dodecagonal duoprisms. Each vertex joins 4 square-dodecagonal duoprisms and 1 dodecagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

This polyteron can be alternated into a hexagonal duoantiprismatic antiprism, although it cannot be made uniform. Half of the dodecagons can also be alternated into long ditrigons to create a hexagonal-hexagonal prismatic prismantiprismoid, which is also nonuniform.

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

Representations
A dodecagonal duoprismatic prism has the following Coxeter diagrams:
 * x x12o x12o (full symmetry)
 * x x6x x6x (dodecagons as dihexagons)
 * xx12oo xx12oo&#x (dodecagonal duoprism atop dodecagonal duoprism)
 * xx6xx xx6xx&#x