# Great dodecahemidodecahedron

Great dodecahemidodecahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Gidhid |

Coxeter diagram | (x5/3x5/3o5/2*a)/2 ( )/2 |

Elements | |

Faces | 12 pentagrams, 6 decagrams |

Edges | 60 |

Vertices | 30 |

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

Measures (edge length 1) | |

Circumradius | |

Dihedral angle | |

Number of external pieces | 420 |

Level of complexity | 22 |

Related polytopes | |

Army | Id, edge length |

Regiment | Gid |

Dual | Great dodecahemidodecacron |

Conjugate | Small dodecahemidodecahedron |

Abstract & topological properties | |

Flag count | 240 |

Euler characteristic | –12 |

Orientable | No |

Genus | 14 |

Properties | |

Symmetry | H_{3}, order 120 |

Flag orbits | 2 |

Convex | No |

Nature | Tame |

The **great dodecahemidodecahedron**, or **gidhid**, is a quasiregular polyhedron and one of 10 uniform hemipolyhedra. It consists of 12 pentagrams and 6 "hemi" decagrams, with two of each joining at a vertex. It can be derived as a rectified petrial great icosahedron.

It is a faceting of the great icosidodecahedron, keeping the original's pentagrams while also using its equatorial decagrams.

It is notable as the only non-regular uniform polyhedron to use exclusively star polygons as faces.

## Name[edit | edit source]

Its pentagrammic faces, as well as its decagrammic faces, are parallel to those of a dodecahedron, hence the name "dodecahemidodecahedron". The "great" modifier, used for stellations in general, distinguishes it from the small dodecahemidodecahedron, which also has this face arrangement.

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category 3: Quasiregulars" (#31).

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

- Klitzing, Richard. "gidhid".
- Wikipedia contributors. "Great dodecahemidodecahedron".
- McCooey, David. "Great dodecahemidodecahedron"