# Hexagonal-decagonal duoprism

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Hexagonal-decagonal duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Bowers style acronym | Hadedip |

Info | |

Coxeter diagram | x6o x10o |

Symmetry | G2×I2(10), order 240 |

Army | Hadedip |

Regiment | Hadedip |

Elements | |

Vertex figure | Digonal disphenoid, edge lengths √3 (base 1), √(5+√5)/2 (base 2), and √2 (sides) |

Cells | 10 hexagonal prisms, 6 decagonal prisms |

Faces | 60 squares, 10 hexagons, 6 decagons |

Edges | 60+60 |

Vertices | 60 |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Hip–6–hip: 144° |

Dip–10–dip: 120° | |

Dip–4–hip: 90° | |

Central density | 1 |

Euler characteristic | 0 |

Number of pieces | 16 |

Level of complexity | 6 |

Related polytopes | |

Dual | Hexagonal-decagonal duotegum |

Conjugate | Hexagonal-decagrammic duoprism |

Properties | |

Convex | Yes |

Orientable | Yes |

Nature | Tame |

The **hexagonal-decagonal duoprism** or **hadedip**, also known as the **6-10 duoprism**, is a uniform duoprism that consists of 6 decagonal prisms and 10 hexagonal prisms, with two of each joining at each vertex.

This polychoron can be alternated into a triangular-pentagonal duoantiprism, although it cannot be made uniform.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a hexagonal-decagonal duoprism with edge length 1 are given by:

## Representations[edit | edit source]

A hexagonal-decagonal duoprism has the following Coxeter diagrams:

- x6o x10o (full symmetry)
- x3x x10o (hexagons as ditrigons)
- x5x x6o (decagons as dipentagons)
- x3x x5x (both applied)
- xux xxx10ooo&#xt (decagonal axial)
- xux xxx5xxx&#xt (dipentagonal axial)

## External links[edit | edit source]

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

- Klitzing, Richard. "Hadedip".