# Enneagonal-dodecagrammic duoprism

(Redirected from 12/5-9 duoprism)

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Enneagonal-dodecagrammic duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Info | |

Coxeter diagram | x9o x12/5o |

Symmetry | I2(9)×I2(12), order 432 |

Army | Semi-uniform etwadip |

Elements | |

Vertex figure | Digonal disphenoid, edge lengths 2cos(π/9) (base 1), (√6–√2)/2 (base 2), √2 (sides) |

Cells | 12 enneagonal prisms, 9 dodecagrammic prisms |

Faces | 108 squares, 12 enneagons, 9 dodecagrams |

Edges | 108+108 |

Vertices | 108 |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Ep–9–ep: 30° |

12/5p–12/5–12/5p: 140° | |

Ep–4–12/5p: 90° | |

Central density | 5 |

Related polytopes | |

Dual | Enneagonal-dodecagrammic duotegum |

Conjugates | Enneagonal-dodecagonal duoprism, Enneagrammic-dodecagonal duoprism, Enneagrammic-dodecagrammic duoprism, Great enneagrammic-dodecagonal duoprism, Great enneagrammic-dodecagrammic duoprism |

Properties | |

Convex | No |

Orientable | Yes |

Nature | Tame |

The **enneagonal-dodecagrammic duoprism**, also known as the **9-12/5 duoprism**, is a uniform duoprism that consists of 12 enneagonal prisms and 9 dodecagrammic prisms, with 2 of each meeting at each vertex.

## Vertex coordinates[edit | edit source]

The coordinates of a enneagonal-dodecagrammic duoprism, centered at the origin and with edge length 2sin(π/9), are given by:

- (1, 0, ±sin(π/9)(√3–1), ±sin(π/9)(√3–1)),
- (1, 0, ±sin(π/9), ±sin(π/9)(2–√3)),
- (1, 0, ±sin(π/9)(2–√3), ±sin(π/9)),
- (cos(2π/9), ±sin(2π/9), ±sin(π/9)(√3–1), ±sin(π/9)(√3–1)),
- (cos(2π/9), ±sin(2π/9), ±sin(π/9), ±sin(π/9)(2–√3)),
- (cos(2π/9), ±sin(2π/9), ±sin(π/9)(2–√3), ±sin(π/9)),
- (cos(4π/9), ±sin(4π/9), ±sin(π/9)(√3–1), ±sin(π/9)(√3–1)),
- (cos(4π/9), ±sin(4π/9), ±sin(π/9), ±sin(π/9)(2–√3)),
- (cos(4π/9), ±sin(4π/9), ±sin(π/9)(2–√3), ±sin(π/9)),
- (–1/2, ±√3/2, ±sin(π/9)(√3–1), ±sin(π/9)(√3–1)),
- (–1/2, ±√3/2, ±sin(π/9), ±sin(π/9)(2–√3)),
- (–1/2, ±√3/2, ±sin(π/9)(2–√3), ±sin(π/9)),
- (cos(8π/9), ±sin(8π/9), ±sin(π/9)(√3–1), ±sin(π/9)(√3–1)),
- (cos(8π/9), ±sin(8π/9), ±sin(π/9), ±sin(π/9)(2–√3)),
- (cos(8π/9), ±sin(8π/9), ±sin(π/9)(2–√3), ±sin(π/9)).

## External links[edit | edit source]

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

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