# Great icosihemidodecahedron

Great icosihemidodecahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Geihid |

Coxeter diagram | (o3/2x5/3x3*a)/2 ( )/2 |

Elements | |

Faces | 20 triangles, 6 decagrams |

Edges | 60 |

Vertices | 30 |

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

Measures (edge length 1) | |

Circumradius | |

Dihedral angle | |

Number of external pieces | 540 |

Level of complexity | 28 |

Related polytopes | |

Army | Id, edge length |

Regiment | Gid |

Dual | Great icosihemidodecacron |

Conjugate | Small icosihemidodecahedron |

Abstract & topological properties | |

Flag count | 240 |

Euler characteristic | –4 |

Orientable | No |

Genus | 6 |

Properties | |

Symmetry | H_{3}, order 120 |

Flag orbits | 2 |

Convex | No |

Nature | Tame |

The **great icosihemidodecahedron**, or **geihid**, is a quasiregular polyhedron and one of 10 uniform hemipolyhedra. It consists of 20 equilateral triangles and 6 "hemi" decagrams, with two of each joining at a vertex.

It can be derived as a rectified petrial great stellated dodecahedron.

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

## Name[edit | edit source]

Its face planes are the same as those of an icosahedron and a dodecahedron in the dual configuration, hence the name "icosihemidodecahedron". The "great" prefix, used for stellations in general, distinguishes it from the small icosihemidodecahedron, 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" (#32).

- Bowers, Jonathan. "Batch 3: Id, Did, and Gid Facetings" (#2 under gid).

- Klitzing, Richard. "geihid".
- Wikipedia contributors. "Great icosihemidodecahedron".
- McCooey, David. "Great Icosihemidodecahedron"