# Pentagonal-hendecagonal duoprism

(Redirected from 11-5 duoprism)

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The **pentagonal-hendecagonal duoprism** or **pahendip**, also known as the **5-11 duoprism**, is a uniform duoprism that consists of 5 hendecagonal prisms and 11 pentagonal prisms, with two of each joining at each vertex.

## Vertex coordinates[edit | edit source]

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

- (±sin(π/11), –sin(π/11)√(5+2√5)/5, 1, 0),
- (±sin(π/11), –sin(π/11)√(5+2√5)/5, cos(2π/11), ±sin(2π/11)),
- (±sin(π/11), –sin(π/11)√(5+2√5)/5, cos(4π/11), ±sin(4π/11)),
- (±sin(π/11), –sin(π/11)√(5+2√5)/5, cos(6π/11), ±sin(6π/11)),
- (±sin(π/11), –sin(π/11)√(5+2√5)/5, cos(8π/11), ±sin(8π/11)),
- (±sin(π/11), –sin(π/11)√(5+2√5)/5, cos(10π/11), ±sin(10π/11)),
- (±sin(π/11)(1+√5)/2, sin(π/11)√(5–√5)/10, 1, 0),
- (±sin(π/11)(1+√5)/2, sin(π/11)√(5–√5)/10, cos(2π/11), ±sin(2π/11)),
- (±sin(π/11)(1+√5)/2, sin(π/11)√(5–√5)/10, cos(4π/11), ±sin(4π/11)),
- (±sin(π/11)(1+√5)/2, sin(π/11)√(5–√5)/10, cos(6π/11), ±sin(6π/11)),
- (±sin(π/11)(1+√5)/2, sin(π/11)√(5–√5)/10, cos(8π/11), ±sin(8π/11)),
- (±sin(π/11)(1+√5)/2, sin(π/11)√(5–√5)/10, cos(10π/11), ±sin(10π/11)),
- (0, 2sin(π/11)√(5+√5)/10, 1, 0),
- (0, 2sin(π/11)√(5+√5)/10, cos(2π/11), ±sin(2π/11)),
- (0, 2sin(π/11)√(5+√5)/10, cos(4π/11), ±sin(4π/11)),
- (0, 2sin(π/11)√(5+√5)/10, cos(6π/11), ±sin(6π/11)),
- (0, 2sin(π/11)√(5+√5)/10, cos(8π/11), ±sin(8π/11)),
- (0, 2sin(π/11)√(5+√5)/10, cos(10π/11), ±sin(10π/11)).

## External links[edit | edit source]

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