Decagrammic-dodecagonal duoprism

The decagrammic-dodecagonal duoprism, also known as staditwadip or the 10/3-12 duoprism, is a uniform duoprism that consists of 12 decagrammic prisms and 10 dodecagonal prisms, with 2 of each at each vertex.

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

Representations
A decagrammic-dodecagonal duoprism has the following Coxeter diagrams:
 * x10/3o x12o (full symmetry)
 * x6x x10/3o (G2×I2(10) symmetry, dodecagons as dihexagons)