Hendecagrammic-dodecagrammic duoprism

The hendecagrammic-dodecagrammic duoprism, also known as the 11/3-12/5 duoprism, is a uniform duoprism that consists of 12 hendecagrammic prisms and 11 dodecagrammic prisms, with 2 of each at each vertex.

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

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