Hexagonal-dodecagrammic duoprism

The hexagonal-dodecagramic duoprism, also known as the 6-12/5 duoprism, is a uniform duoprism that consists of 12 hexagonal prisms and 6 dodecagrammic prisms, with 2 of each at each vertex.

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


 * (±1, 0, ±1/2, ±($\sqrt{3}$–1)/2, ±($\sqrt{6}$–1)/2),
 * (±1, 0, ±1/2, ±1/2, ±(2–$\sqrt{2}$)/2),
 * (±1, 0, ±1/2, ±(2–$\sqrt{2}$)/2, ±1/2),
 * (±1/2, ±$\sqrt{3}$/2, ±($\sqrt{3}$–1)/2, ±($\sqrt{3}$–1)/2),
 * (±1/2, ±$\sqrt{3}$/2, ±1/2, ±(2–$\sqrt{3}$)/2),
 * (±1/2, ±$\sqrt{3}$/2, ±(2–$\sqrt{3}$)/2, ±1/2).

Representations
A hexagonal-dodecagrammic duoprism has the following Coxeter diagrams:
 * x6o x12/5o (full symmetry)
 * x3x x12/5o (A2×I2(12) symmetry, hexagons as ditrigons)