# Great icosidodecahedron

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Great icosidodecahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Gid |

Coxeter diagram | o5/2x3o () |

Elements | |

Faces | 20 triangles, 12 pentagrams |

Edges | 60 |

Vertices | 30 |

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

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angle | |

Central density | 7 |

Number of external pieces | 132 |

Level of complexity | 10 |

Related polytopes | |

Army | Id, edge length |

Regiment | Gid |

Dual | Great rhombic triacontahedron |

Conjugate | Icosidodecahedron |

Convex core | Icosahedron |

Abstract & topological properties | |

Flag count | 240 |

Euler characteristic | 2 |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | H_{3}, order 120 |

Flag orbits | 2 |

Convex | No |

Nature | Tame |

The **great icosidodecahedron** or **gid** is a quasiregular uniform polyhedron. It consists of 20 equilateral triangles and 12 pentagrams, with two of each joining at a vertex. It can be derived as a rectified great stellated dodecahedron or great icosahedron.

## Vertex coordinates[edit | edit source]

A great icosidodecahedron of side length 1 has vertex coordinates given by all permutations of

- ,

and even permutations of

- .

The first set of vertices corresponds to a scaled octahedron which can be inscribed into the great icosidodecahedron.

## Related polyhedra[edit | edit source]

The great icosidodecahedron is the colonel of a three-member regiment that also includes the great icosihemidodecahedron and great dodecahemidodecahedron.

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category 3: Quasiregulars" (#30).

- Bowers, Jonathan. "Batch 3: Id, Did, and Gid Facetings" (#1 under gid).

- Klitzing, Richard. "gid".
- Wikipedia contributors. "Great icosidodecahedron".
- McCooey, David. "Great Icosidodecahedron"