# Great icosicosidodecahedron

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Great icosicosidodecahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Giid |

Coxeter diagram | o3/2x3x5*a () |

Elements | |

Faces | 20 triangles, 12 pentagons, 20 hexagons |

Edges | 60+60 |

Vertices | 60 |

Vertex figure | Crossed isosceles trapezoid, edge lengths 1, √3, (1+√5)/2, √3 |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 5–6: |

3–6: | |

Central density | 6 |

Number of external pieces | 1232 |

Level of complexity | 75 |

Related polytopes | |

Army | Tid, edge length |

Regiment | Gidditdid |

Dual | Great icosacronic hexecontahedron |

Conjugate | Small icosicosidodecahedron |

Convex core | Icosahedron |

Abstract & topological properties | |

Flag count | 480 |

Euler characteristic | –8 |

Orientable | Yes |

Genus | 5 |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

The **great icosicosidodecahedron**, or **giid**, is a uniform polyhedron. It consists of 20 triangles, 12 pentagons, and 20 hexagons. One triangle, one pentagon, and two hexagons join at each vertex.

It is a faceting of the great ditrigonal dodecicosidodecahedron, using its 12 pentagons and 20 triangles along with 20 additional hexagons.

A semi-uniform variant of this polyhedron can be constructed as a rectified great ditrigonary icosidodecahedron.

## Vertex coordinates[edit | edit source]

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

## Related polyhedra[edit | edit source]

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category 4: Trapeziverts" (#49).

- Klitzing, Richard. "giid".
- Wikipedia contributors. "Great icosicosidodecahedron".
- McCooey, David. "Great Icosicosidodecahedron"