Square-dodecagonal duoprism

The square-dodecagonal duoprism or sitwadip, also known as the 4-12 duoprism, is a uniform duoprism that consists of 4 dodecagonal prisms, 12 cubes, with two of each joining at each vertex. It is also a convex segmentochoron, being the prism of the dodecagonal prism.

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

This polychoron can be subsymmetrically faceted into a 12-3 step prism, although it cannot be made uniform.

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

Representations
A square-dodecagonal duoprism has the following Coxeter diagrams:


 * x4o x12o (full symmetry)
 * x x x12o (squares as rectangles)
 * x4o x6x (dodecagons as dihexagons)
 * x x x6x (both rectangles and dihexagons)