# Great dodecahemicosahedron

Great dodecahemicosahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Gidhei |

Coxeter diagram | (o5/4x3x5*a)/2 ()/2 |

Elements | |

Faces | 12 pentagons, 10 hexagons |

Edges | 60 |

Vertices | 30 |

Vertex figure | Bowtie, edge lengths (1+√5)/2 and √3 |

Measures (edge length 1) | |

Circumradius | 1 |

Dihedral angle | |

Number of external pieces | 312 |

Level of complexity | 18 |

Related polytopes | |

Army | Id, edge length |

Regiment | Did |

Dual | Great dodecahemicosacron |

Conjugate | Small dodecahemicosahedron |

Abstract & topological properties | |

Flag count | 240 |

Euler characteristic | –8 |

Orientable | No |

Genus | 10 |

Properties | |

Symmetry | H_{3}, order 120 |

Flag orbits | 2 |

Convex | No |

Nature | Tame |

The **great dodecahemicosahedron**, or **gidhei**, is a quasiregular polyhedron and one of 10 uniform hemipolyhedra. It consists of 12 pentagons and 10 "hemi" hexagons, passing through its center, with two of each joining at a vertex.

It can be constructed as the rectification of the Petrial small stellated dodecahedron.

It is a faceting of the dodecadodecahedron, keeping the original's pentagons while also using its equatorial hexagons.

## Name[edit | edit source]

Its pentagonal faces are parallel to those of a dodecahedron, and its hemi hexagonal faces are parallel to those of an icosahedron, hence the name "dodecahemicosahedron". The "great" modifier, used for stellations in general, distinguishes it from the small dodecahemicosahedron, which also has this face arrangement.

## Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the dodecadodecahedron.

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category 3: Quasiregulars" (#29).

- Bowers, Jonathan. "Batch 3: Id, Did, and Gid Facetings" (#3 under did).

- Klitzing, Richard. "gidhei".
- Wikipedia contributors. "Great dodecahemicosahedron".
- McCooey, David. "Great Dodecahemicosahedron"