Dodecagonal duoprism

The dodecagonal duoprism or twaddip, also known as the dodecagonal-dodecagonal duoprism, the 12 duoprism or the 12-12 duoprism, is a noble uniform duoprism that consists of 24 dodecagonal prisms, with 4 joining at each vertex. It is also the 24-11 gyrochoron. It is the first in an infinite family of isogonal dodecagonal dihedral swirlchora and also the first in an infinite family of isochoric dodecagonal hosohedral swirlchora.

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

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

Variations
A dodecagonal duoprism has the following Coxeter diagrams:


 * x12o x12o (full symmetry)
 * x6x x12o (one dodecagon as dihexagon)
 * x6x x6x (both dodecagons as dihexagons)