# Hexagonal-enneagonal duoprism

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Hexagonal-enneagonal duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Hendip |

Coxeter diagram | x6o x9o () |

Elements | |

Cells | 9 hexagonal prisms, 6 enneagonal prisms |

Faces | 54 squares, 9 hexagons, 6 enneagons |

Edges | 54+54 |

Vertices | 54 |

Vertex figure | Digonal disphenoid, edge lengths √3 (base 1), 2cos(π/9) (base 2), and √2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Hip–6–hip: 140° |

Ep–9–ep: 120° | |

Hip–4–ep: 90° | |

Central density | 1 |

Number of external pieces | 15 |

Level of complexity | 6 |

Related polytopes | |

Army | Hendip |

Regiment | Hendip |

Dual | Hexagonal-enneagonal duotegum |

Conjugates | Hexagonal-enneagrammic duoprism, Hexagonal-great enneagrammic duoprism |

Abstract & topological properties | |

Flag count | 1296 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | G_{2}×I_{2}(9), order 216 |

Flag orbits | 6 |

Convex | Yes |

Nature | Tame |

The **hexagonal-enneagonal duoprism** or **hendip**, also known as the **6-9 duoprism**, is a uniform duoprism that consists of 6 enneagonal prisms and 9 hexagonal prisms, with two of each joining at each vertex.

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

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

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

- ,
- ,
- ,
- ,
- ,
- ,

where j = 2, 4, 8.

## Representations[edit | edit source]

A hexagonal-enneagonal duoprism has the following Coxeter diagrams:

- x6o x9o () (full symmetry)
- x3x x9o () (A
_{2}×I_{2}(9) symmetry, hexagons as ditrigons)

## External links[edit | edit source]

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

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