# Enneagonal duoprism

Jump to navigation
Jump to search

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

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Edip |

Coxeter diagram | x9o x9o () |

Elements | |

Cells | 18 enneagonal prisms |

Faces | 81 squares, 18 enneagons |

Edges | 162 |

Vertices | 81 |

Vertex figure | Tetragonal disphenoid, edge lengths 2cos(π/9) (bases) and √2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Hypervolume | |

Dichoral angles | Ep–9–ep: 140° |

Ep–4–ep: 90° | |

Central density | 1 |

Number of external pieces | 18 |

Level of complexity | 3 |

Related polytopes | |

Army | Edip |

Regiment | Edip |

Dual | Enneagonal duotegum |

Conjugates | Enneagrammic duoprism, Great enneagrammic duoprism |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(9)≀S_{2}, order 648 |

Convex | Yes |

Nature | Tame |

The **enneagonal duoprism** or **edip**, also known as the **enneagonal-enneagonal duoprism**, the **9 duoprism** or the **9-9 duoprism**, is a noble uniform duoprism that consists of 18 enneagonal prisms, with 4 joining at each vertex. It is also the 18-8 gyrochoron. It is the first in an infinite family of isogonal enneagonal dihedral swirlchora and also the first in an infinite family of isochoric enneagonal hosohedral swirlchora.

This polychoron can be subsymmetrically faceted into a triangular triswirlprism, although it cannot be made uniform.

## Gallery[edit | edit source]

Wireframe, cell, net

## Vertex coordinates[edit | edit source]

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

where j, k = 2, 4, 8.

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

## External links[edit | edit source]

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

- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".

- Klitzing, Richard. "n-n-dip".