# Great inverted disnub icosidodecahedron

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Great inverted disnub icosidodecahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Gidsid |

Elements | |

Components | 2 great inverted snub icosidodecahedra |

Faces | 120 triangles, 40 triangles as 20 hexagrams, 24 pentagrams as 12 stellated decagrams |

Edges | 60+120+120 |

Vertices | 120 |

Vertex figure | Irregular pentagon, edge lengths 1, 1, 1, 1, (√5–1)/2 |

Measures (edge length 1) | |

Circumradius | ≈ 0.64502 |

Volume | ≈ 5.42774 |

Dihedral angles | 3–3: ≈ 89.78760° |

5/2–3: ≈ 21.61047° | |

Central density | 26 |

Number of external pieces | 1560 |

Level of complexity | 100 |

Related polytopes | |

Army | Semi-uniform Grid |

Regiment | Gidsid |

Dual | Compound of two great inverted pentagonal hexecontahedra |

Conjugates | Disnub icosidodecahedron, great disnub icosidodecahedron, great diretrosnub icosidodecahedron |

Convex core | Order-6-truncated disdyakis triacontahedron |

Abstract & topological properties | |

Flag count | 1200 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

The **great inverted disnub icosidodecahedron**, **gidsid**, or **compound of two great inverted snub icosidodecahedra** is a uniform polyhedron compound. It consists of 120 snub triangles, 40 further triangles, and 24 pentagrams (the latter two can combine in pairs due to faces in the same plane). Four triangles and one pentagram join at each vertex.

Its quotient prismatic equivalent is the great inverted snub icosidodecahedral antiprism, which is four-dimensional.

## Measures[edit | edit source]

The circumradius of the great inverted disnub icosidodecahedron with unit edge length is the second to smallest positive real root of:

Its volume is given by the third largest positive real root of:

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category C10: Disnubs" (#73).

- Klitzing, Richard. "gidsid".

- Wikipedia Contributors. "Compound of two great inverted snub icosidodecahedra".