Decagonal-hendecagrammic duoprism

The decagonal-hendecagrammic duoprism, also known as the 10-11/3 duoprism, is a uniform duoprism that consists of 11 decagonal prisms and 10 hendecagrammic prisms, with 2 of each at each vertex.

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

Vertex coordinates
The coordinates of a decagonal-hendecagrammic duoprism, centered at the origin and with edge length 2sin(3π/11), are given by: where j = 2, 4, 6, 8, 10.
 * $$\left(±\sin\frac{3\pi}{11},\,±\sqrt{5+2\sqrt5}\sin\frac{3\pi}{11},\,1,\,0\right),$$
 * $$\left(±\sin\frac{3\pi}{11},\,±\sqrt{5+2\sqrt5}\sin\frac{3\pi}{11},\,\cos\left(\frac{j\pi}{11}\right),\,±\sin\left(\frac{j\pi}{11}\right)\right),$$
 * $$\left(±\frac{3+\sqrt5}2\sin\frac{3\pi}{11},\,±\sqrt{\frac{5+\sqrt5}2}\sin\frac{3\pi}{11},\,1,\,0\right),$$
 * $$\left(±\frac{3+\sqrt5}2\sin\frac{3\pi}{11},\,±\sqrt{\frac{5+\sqrt5}2}\sin\frac{3\pi}{11},\,\cos\left(\frac{j\pi}{11}\right),\,±\sin\left(\frac{j\pi}{11}\right)\right),$$
 * $$\left(±\left(1+\sqrt5\right)\sin\frac{3\pi}{11},\,0,\,1,\,0\right),$$
 * $$\left(±\left(1+\sqrt5\right)\sin\frac{3\pi}{11},\,0,\,\cos\left(\frac{j\pi}{11}\right),\,±\sin\left(\frac{j\pi}{11}\right)\right),$$

Representations
A decagonal-hendecagrammic duoprism has the following Coxeter diagrams:
 * x10o x11/3o (full symmetry)
 * x5x x11/3o (H2×I2(11) symmetry, decagons as dipentagons)