# Hendecagonal-dodecagonal duoprism

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The **hendecagonal-dodecagonal duoprism** or **hentwadip**, also known as the **11-12 duoprism**, is a uniform duoprism that consists of 11 dodecagonal prisms and 12 hendecagonal prisms, with two of each joining at each vertex.

## Vertex coordinates[edit | edit source]

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

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

## Representations[edit | edit source]

A hendecagonal-dodecagonal duoprism has the following Coxeter diagrams:

- x11o x12o (full symmetry)
- x6x x11o (dodecagons as dihexagons)

## External links[edit | edit source]

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