Decagonal-dodecagonal duoprism

The decagonal-dodecagonal duoprism or datwadip, also known as the 10-12 duoprism, is a uniform duoprism that consists of 10 dodecagonal prisms and 12 decagonal prisms, with two of each joining at each vertex.

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

Vertex coordinates
The coordinates of a decagonal-dodecagonal duoprism of edge length 1, centered at the origin, are given by:
 * $$\left(0,\,±\frac{1+\sqrt5}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2}\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{2},\,±\frac12,\,±\frac{2+\sqrt3}{2}\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{2},\,±\frac{2+\sqrt3}{2},\,±\frac12\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2}\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4},\,±\frac12,\,±\frac{2+\sqrt3}{2}\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4},\,±\frac{2+\sqrt3}{2},\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12,\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2}\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12,\,±\frac12,\,±\frac{2+\sqrt3}{2}\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac12\right).$$

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


 * x10o x12o (full symmetry)
 * x5x x12o (decagons as dipentagons)
 * x6x x10o (dodecagons as dihexagons)
 * x5x x6x (both of these applied)