Dodecagonal duotegum

The dodecagonal duotegum or twaddit, also known as the dodecagonal-dodecagonal duotegum, the 12 duotegum, or the 12-12 duotegum, is a noble duotegum that consists of 144 tetragonal disphenoids and 24 vertices, with 24 cells joining at each vertex. . It is also the 24-11 step prism. It is the first in an infinite family of isogonal dodecagonal hosohedral swirlchora and also the first in an infinite family of isochoric dodecagonal dihedral swirlchora.

Vertex coordinates
The vertices of a dodecagonal duotegum based on 2 dodecagons of edge length 1, centered at the origin, are given by:


 * $$\left(±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,0,\,0\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt3}{2},\,0,\,0\right),$$
 * $$\left(±\frac{2+\sqrt3}{2},\,±\frac12,\,0,\,0\right),$$
 * $$\left(0,\,0,\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2}\right),$$
 * $$\left(0,\,0,\,±\frac12,\,±\frac{2+\sqrt3}{2}\right),$$
 * $$\left(0,\,0,\,±\frac{2+\sqrt3}{2},\,±\frac12\right).$$