# Grand hendecagrammic-dodecagrammic duoprism

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The **grand hendecagrammic-dodecagrammic duoprism**, also known as the **11/5-12/5 duoprism**, is a uniform duoprism that consists of 12 grand hendecagrammic prisms and 11 dodecagrammic prisms, with 2 of each meeting at each vertex.

## Coordinates[edit | edit source]

The vertex coordinates of a grand hendecagrammic-dodecagrammic duoprism, centered at the origin and with edge length 2sin(5π/11), are given by:

- (1, 0, ±sin(5π/11)(√3–1), ±sin(5π/11)(√3–1)),
- (1, 0, ±sin(5π/11), ±sin(5π/11)(2–√3)),
- (1, 0, ±sin(5π/11)(2–√3), ±sin(5π/11)),
- (cos(2π/11), ±sin(2π/11), ±sin(5π/11)(√3–1), ±sin(5π/11)(√3–1)),
- (cos(2π/11), ±sin(2π/11), ±sin(5π/11), ±sin(5π/11)(2–√3)),
- (cos(2π/11), ±sin(2π/11), ±sin(5π/11)(2–√3), ±sin(5π/11)),
- (cos(4π/11), ±sin(4π/11), ±sin(5π/11)(√3–1), ±sin(5π/11)(√3–1)),
- (cos(4π/11), ±sin(4π/11), ±sin(5π/11), ±sin(5π/11)(2–√3)),
- (cos(4π/11), ±sin(4π/11), ±sin(5π/11)(2–√3), ±sin(5π/11)),
- (cos(6π/11), ±sin(6π/11), ±sin(5π/11)(√3–1), ±sin(5π/11)(√3–1)),
- (cos(6π/11), ±sin(6π/11), ±sin(5π/11), ±sin(5π/11)(2–√3)),
- (cos(6π/11), ±sin(6π/11), ±sin(5π/11)(2–√3), ±sin(5π/11)),
- (cos(8π/11), ±sin(8π/11), ±sin(5π/11)(√3–1), ±sin(5π/11)(√3–1)),
- (cos(8π/11), ±sin(8π/11), ±sin(5π/11), ±sin(5π/11)(2–√3)),
- (cos(8π/11), ±sin(8π/11), ±sin(5π/11)(2–√3), ±sin(5π/11)),
- (cos(10π/11), ±sin(10π/11), ±sin(5π/11)(√3–1), ±sin(5π/11)(√3–1)),
- (cos(10π/11), ±sin(10π/11), ±sin(5π/11), ±sin(5π/11)(2–√3)),
- (cos(10π/11), ±sin(10π/11), ±sin(5π/11)(2–√3), ±sin(5π/11)).

## External links[edit | edit source]

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

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