# Hendecagrammic-dodecagonal duoprism

Revision as of 03:08, 20 December 2020 by The New Kid (talk | contribs)

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.

## Vertex coordinates[edit | edit source]

The 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+√3), ±sin(3π/11)(1+√3)),
- (1, 0, ±sin(3π/11), ±sin(3π/11)(2+√3)),
- (1, 0, ±sin(3π/11)(2+√3), ±sin(3π/11)),
- (cos(2π/11), ±sin(2π/11), ±sin(3π/11)(1+√3), ±sin(3π/11)(1+√3)),
- (cos(2π/11), ±sin(2π/11), ±sin(3π/11), ±sin(3π/11)(2+√3)),
- (cos(2π/11), ±sin(2π/11), ±sin(3π/11)(2+√3), ±sin(3π/11)),
- (cos(4π/11), ±sin(4π/11), ±sin(3π/11)(1+√3), ±sin(3π/11)(1+√3)),
- (cos(4π/11), ±sin(4π/11), ±sin(3π/11), ±sin(3π/11)(2+√3)),
- (cos(4π/11), ±sin(4π/11), ±sin(3π/11)(2+√3), ±sin(3π/11)),
- (cos(6π/11), ±sin(6π/11), ±sin(3π/11)(1+√3), ±sin(3π/11)(1+√3)),
- (cos(6π/11), ±sin(6π/11), ±sin(3π/11), ±sin(3π/11)(2+√3)),
- (cos(6π/11), ±sin(6π/11), ±sin(3π/11)(2+√3), ±sin(3π/11)),
- (cos(8π/11), ±sin(8π/11), ±sin(3π/11)(1+√3), ±sin(3π/11)(1+√3)),
- (cos(8π/11), ±sin(8π/11), ±sin(3π/11), ±sin(3π/11)(2+√3)),
- (cos(8π/11), ±sin(8π/11), ±sin(3π/11)(2+√3), ±sin(3π/11)),
- (cos(10π/11), ±sin(10π/11), ±sin(3π/11)(1+√3), ±sin(3π/11)(1+√3)),
- (cos(10π/11), ±sin(10π/11), ±sin(3π/11), ±sin(3π/11)(2+√3)),
- (cos(10π/11), ±sin(10π/11), ±sin(3π/11)(2+√3), ±sin(3π/11)).

## External links[edit | edit source]

- Bowers, Jonathan. "Category A: Duoprisms".

This article is a stub. You can help Polytope Wiki by expanding it. |