Dodecagonal prism

The dodecagonal prism, or twip, is a prismatic uniform polyhedron. It consists of 2 dodecagons and 12 squares. Each vertex joins one dodecagon and two squares. As the name suggests, it is a prism based on a dodecagon.

Vertex coordinates
A dodecagonal prism of edge length 1 has vertex coordinates given by:
 * (±(1+$\sqrt{9+4√3}$)/2, ±(1+$\sqrt{3}$)/2, ±1/2),
 * (±1/2, ±(2+$\sqrt{2}$)/2, ±1/2),
 * (±(2+$\sqrt{2}$)/2, ±1/2, ±1/2).

Representations
A dodecagonal prism has the following Coxeter diagrams:


 * x x12o (full symmetry)
 * x x6x (generally a dihexagonal prism)
 * s2s12x (generally a dihexagonal trapezoprism)
 * xx12oo&#x (bases esen separately)
 * xx6xx&#x

Variations
There are several isogonal lower-symmetry variants of the dodecagonal prism, all of which are listed below:

Dihexagonal prism
A dihexagonal prism is a prism based on a dihexagon. The two bases are dihexagons, while the lateral sides are 6+6 rectangles.

Dihexagonal trapezoprism
A dihexagonal trapezoprism is made out of two opposite dihexagons in parallel planes, connected by 12 isosceles trapezoids.