Hendecagrammic-dodecagonal duoprism

The hendecagrammic-dodecagonal duoprism, also known as the 11/3-12 duoprism, is a uniform duoprism that consists of 12 hendecagrammic prisms and 11 dodecagonal prisms, with 2 of each at each vertex.

The name can also refer to the small hendecagrammic-dodecagonal duoprism, the great hendecagrammic-dodecagonal duoprism, or the grand hendecagrammic-dodecagonal duoprism.

Vertex coordinates
The coordinates of a hendecagrammic-dodecagonal duoprism, centered at the origin and with edge length 2sin(3π/11), are given by: where j = 2, 4, 6, 8, 10.
 * $$\left(1,\,0,\,±\left(1+\sqrt3\right)\sin\frac{3\pi}{11},\,±\left(1+\sqrt3\right)\sin\frac{3\pi}{11}\right),$$
 * $$\left(1,\,0,\,±\sin\frac{3\pi}{11},\,±\left(2+\sqrt3\right)\sin\frac{3\pi}{11}\right),$$
 * $$\left(1,\,0,\,±\left(2+\sqrt3\right)\sin\frac{3\pi}{11},\,±\sin\frac{3\pi}{11}\right),$$
 * $$\left(\cos\left(\frac{j\pi}{11}\right),\,±\sin\left(\frac{j\pi}{11}\right),\,±\left(1+\sqrt3\right)\sin\frac{3\pi}{11},\,±\left(1+\sqrt3\right)\sin\frac{3\pi}{11}\right),$$
 * $$\left(\cos\left(\frac{j\pi}{11}\right),\,±\sin\left(\frac{j\pi}{11}\right),\,±\sin\frac{3\pi}{11},\,±\left(2+\sqrt3\right)\sin\frac{3\pi}{11}\right),$$
 * $$\left(\cos\left(\frac{j\pi}{11}\right),\,±\sin\left(\frac{j\pi}{11}\right),\,±\left(2+\sqrt3\right)\sin\frac{3\pi}{11},\,±\sin\frac{3\pi}{11}\right),$$

Representations
A hendecagrammic-dodecagonal duoprism has the following Coxeter diagrams:
 * x11/3o x12o (full symmetry)
 * x6x x11/3o (G2×I2(11) symmetry, dodecagons as dihexagons)