Dodecagonal-cubic duoprism

The dodecagonal-cubic duoprism or twacube, also known as the square-dodecagonal duoprismatic prism, is a convex uniform duoprism that consists of 12 tesseracts and 6 square-dodecagonal duoprisms. Each vertex joins 2 tesseracts and 3 square-dodecagonal duoprisms. It is a duoprism based on a square and a dodecagonal prism, which makes it a convex segmentoteron.

This polyteron can be alternated into a hexagonal-tetrahedral duoantiprism, although it cannot be made uniform. The dodecagons can also be alternated into long ditrigons to create a tetrahedral-hexagonal prismantiprismoid, which is also nonuniform.

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

Representations
A dodecagonal-cubic duoprism has the following Coxeter diagrams:
 * x12o x4o3o (full symmetry)
 * x x4o x12o (square-dodecagonal duoprismatic prism)
 * x x x x12o (dodecagonal prismatic prismatic prism)