Dodecagrammic duoprism

The dodecagrammic duoprism, also known as the dodecagrammic-dodecagrammic duoprism, the 12/5 duoprism or the 12/5-12/5 duoprism, is a noble uniform duoprism that consists of 24 dodecagrammic prisms, with 4 at each vertex.

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

Representations
A dodecagrammic duoprism has the following Coxeter diagrams:
 * x12/5o x12/5o (full symmetry)
 * x6/5x x12/5o (G2×I2(12) symmetry)
 * x6/5x x6/5x (G2≀S2 symmetry)