Pentagonal-dodecagonal duoprism

The pentagonal-dodecagonal duoprism or pitwadip, also known as the 5-12 duoprism, is a uniform duoprism that consists of 5 dodecagonal prisms and 12 pentagonal prisms, with two of each joining at each vertex.

Vertex coordinates
The coordinates of a pentagonal-dodecagonal duoprism, centered at the origin and with unit edge length, are given by:
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2}\right),$$
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\frac12,\,±\frac{2+\sqrt3}{2}\right),$$
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\frac{2+\sqrt3}{2},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac12,\,±\frac{2+\sqrt3}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac{2+\sqrt3}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2}\right),$$
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac12,\,±\frac{2+\sqrt3}{2}\right),$$
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac{2+\sqrt3}{2},\,±\frac12\right).$$

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


 * x5o x12o (full symmetry)
 * x5o x6x (dodecagons as dihexagons)