# Hexagonal-great rhombicosidodecahedral duoprism

Hexagonal-great rhombicosidodecahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Hagrid |

Coxeter diagram | x6o x5x3x |

Elements | |

Tera | 30 square-hexagonal duoprisms, 20 hexagonal duoprisms, 12 hexagonal-decagonal duoprisms, 6 great rhombicosidodecahedral prisms |

Cells | 180 cubes, 60+60+60+120 hexagonal prisms, 72 decagonal prisms, 6 great rhombicosidodecahedra |

Faces | 180+360+360+360 squares, 120+120 hexagons, 72 decagons |

Edges | 360+360+360+720 |

Vertices | 720 |

Vertex figure | Mirror-symmetric pentachoron, edge lengths √2, √3, √(5+√5)/2 (base triangle), √3 (top edge), √2 (side edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Shiddip–hip–hiddip: |

Shiddip–hip–hadedip: | |

Hiddip–hip–hadedip: | |

Griddip–grid–griddip: 120° | |

Shiddip–cube–griddip: 90° | |

Hiddip–hip–griddip: 90° | |

Hadedip–dip–griddip: 90° | |

Central density | 1 |

Number of external pieces | 68 |

Level of complexity | 60 |

Related polytopes | |

Army | Hagrid |

Regiment | Hagrid |

Dual | Hexagonal-disdyakis triacontahedral duotegum |

Conjugate | Hexagonal-great quasitruncated icosidodecahedral duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}×G_{2}, order 1440 |

Convex | Yes |

Nature | Tame |

The **hexagonal-great rhombicosidodecahedral duoprism** or **hagrid** is a convex uniform duoprism that consists of 6 great rhombicosidodecahedral prisms, 12 hexagonal-decagonal duoprisms, 20 hexagonal duoprisms, and 30 square-hexagonal duoprisms. Each vertex joins 2 great rhombicosidodecahedral prisms, 1 square-hexagonal duoprism, 1 hexagonal duoprism, and 1 hexagonal-decagonal duoprism.

This polyteron can be alternated into a triangular-snub dodecahedral duoantiprism, although it cannot be made uniform.

## Vertex coordinates[edit | edit source]

The vertices of a hexagonal-great rhombicosidodecahedral duoprism of edge length 1 are given by all permutations of the last three coordinates of:

along with all even permutations of the last three coordinates of:

## Representations[edit | edit source]

A hexagonal-great rhombicosidodecahedral duoprism has the following Coxeter diagrams:

- x6o x5x3x (full symmetry)
- x3x x5x3x (hexagons as ditrigons)

## External links[edit | edit source]

- Klitzing, Richard. "hagrid".