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 meeting 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.

Coordinates
The vertex coordinates of a hendecagrammic-dodecagonal duoprism, centered at the origin and with edge length 2sin(3π/11), are given by:


 * (1, 0, ±sin(3π/11)(1+$\sqrt{6}$), ±sin(3π/11)(1+$\sqrt{2}$)),
 * (1, 0, ±sin(3π/11), ±sin(3π/11)(2+$\sqrt{2}$)),
 * (1, 0, ±sin(3π/11)(2+$\sqrt{2+√3+1/[4sin^{2}(3π/11)]}$), ±sin(3π/11)),
 * (cos(2π/11), ±sin(2π/11), ±sin(3π/11)(1+$\sqrt{3}$), ±sin(3π/11)(1+$\sqrt{3}$)),
 * (cos(2π/11), ±sin(2π/11), ±sin(3π/11), ±sin(3π/11)(2+$\sqrt{3}$)),
 * (cos(2π/11), ±sin(2π/11), ±sin(3π/11)(2+$\sqrt{3}$), ±sin(3π/11)),
 * (cos(4π/11), ±sin(4π/11), ±sin(3π/11)(1+$\sqrt{3}$), ±sin(3π/11)(1+$\sqrt{3}$)),
 * (cos(4π/11), ±sin(4π/11), ±sin(3π/11), ±sin(3π/11)(2+$\sqrt{3}$)),
 * (cos(4π/11), ±sin(4π/11), ±sin(3π/11)(2+$\sqrt{3}$), ±sin(3π/11)),
 * (cos(6π/11), ±sin(6π/11), ±sin(3π/11)(1+$\sqrt{3}$), ±sin(3π/11)(1+$\sqrt{3}$)),
 * (cos(6π/11), ±sin(6π/11), ±sin(3π/11), ±sin(3π/11)(2+$\sqrt{3}$)),
 * (cos(6π/11), ±sin(6π/11), ±sin(3π/11)(2+$\sqrt{3}$), ±sin(3π/11)),
 * (cos(8π/11), ±sin(8π/11), ±sin(3π/11)(1+$\sqrt{3}$), ±sin(3π/11)(1+$\sqrt{3}$)),
 * (cos(8π/11), ±sin(8π/11), ±sin(3π/11), ±sin(3π/11)(2+$\sqrt{3}$)),
 * (cos(8π/11), ±sin(8π/11), ±sin(3π/11)(2+$\sqrt{3}$), ±sin(3π/11)),
 * (cos(10π/11), ±sin(10π/11), ±sin(3π/11)(1+$\sqrt{3}$), ±sin(3π/11)(1+$\sqrt{3}$)),
 * (cos(10π/11), ±sin(10π/11), ±sin(3π/11), ±sin(3π/11)(2+$\sqrt{3}$)),
 * (cos(10π/11), ±sin(10π/11), ±sin(3π/11)(2+$\sqrt{3}$), ±sin(3π/11)).