Hendecagrammic-grand hendecagrammic duoprism

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

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

Coordinates
The vertex coordinates of a hendecagrammic-grand hendecagrammic duoprism, centered at the origin and with edge length 4sin(3π/11)sin(5π/11), are given by: where j, k = 2, 4, 6, 8, 10.
 * $$\left(2\sin\frac{5\pi}{11},\,0,\,2\sin\frac{3\pi}{11},\,0\right),$$
 * $$\left(2\sin\frac{5\pi}{11},\,0,\,2\sin\frac{3\pi}{11}\cos\left(\frac{k\pi}{11}\right),\,±2\sin\frac{3\pi}{11}\sin\left(\frac{k\pi}{11}\right)\right),$$
 * $$\left(2\sin\frac{5\pi}{11}\cos\left(\frac{j\pi}{11}\right),\,±2\sin\frac{5\pi}{11}\sin\left(\frac{j\pi}{11}\right),\,2\sin\frac{3\pi}{11},\,0\right),$$
 * $$\left(2\sin\frac{5\pi}{11}\cos\left(\frac{j\pi}{11}\right),\,±2\sin\frac{5\pi}{11}\sin\left(\frac{j\pi}{11}\right),\,2\sin\frac{3\pi}{11}\cos\left(\frac{k\pi}{11}\right),\,±2\sin\frac{3\pi}{11}\sin\left(\frac{k\pi}{11}\right)\right),$$