Hexagonal-dodecagonal duoprism

The hexagonal-dodecagonal duoprism or hitwadip, also known as the 6-12 duoprism, is a uniform duoprism that consists of 6 dodecagonal prisms and 12 hexagonal prisms, with two of each joining at each vertex.

The convex hull of two orthogonal hexagonal-dodecagonal duoprisms is either the hexagonal duoexpandoprism or the hexagonal duotruncatoprism.

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

Vertex coordinates
The vertices of a hexagonal-dodecagonal duoprism of edge length 1, centered at the origin, are given by:
 * $$\left(0,\,±1,\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2}\right),$$
 * $$\left(0,\,±1,\,±\frac12,\,±\frac{2+\sqrt3}{2}\right),$$
 * $$\left(0,\,±1,\,±\frac{2+\sqrt3}{2},\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt3}{2},\,±\frac12,\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2}\right),$$
 * $$\left(±\frac{\sqrt3}{2},\,±\frac12,\,±\frac12,\,±\frac{2+\sqrt3}{2}\right),$$
 * $$\left(±\frac{\sqrt3}{2},\,±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac12\right).$$

representations
A hexagonal=dodecagonal duoprism has the following Coxeter diagrams:


 * x6o x12o (full symmetry)
 * x6x x6o (dodecagons as dihexagons, hexagon duoprism symmetry)
 * x3x x12o (hexagons as ditrigons)
 * x3x x6x (both as above)