# Great inverted snub icosidodecahedron

Great inverted snub icosidodecahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Gisid |

Coxeter diagram | s5/3s3s () |

Elements | |

Faces | 20+60 triangles, 12 pentagrams |

Edges | 30+60+60 |

Vertices | 60 |

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

Measures (edge length 1) | |

Circumradius | ≈ 0.64502 |

Volume | ≈ 2.71387 |

Dihedral angles | 3–3: ≈ 89.78760° |

5/2–3: ≈ 21.61047° | |

Central density | 13 |

Number of external pieces | 780 |

Level of complexity | 65 |

Related polytopes | |

Army | Non-uniform snub dodecahedron |

Regiment | Gisid |

Dual | Great inverted pentagonal hexecontahedron |

Conjugates | Snub dodecahedron, Great snub icosidodecahedron, Great inverted retrosnub icosidodecahedron |

Convex core | Chiral order-6 truncated pentakis dodecahedron |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | H_{3}+, order 60 |

Convex | No |

Nature | Tame |

The **great inverted snub icosidodecahedron** or **gisid**, is a uniform polyhedron. It consists of 60 snub triangles, 20 additional triangles, and 12 pentagrams. Four triangles and one pentagram meet at each vertex. It can be constructed by alternation of the great quasitruncated icosidodecahedron after setting all edge lengths to be equal.

## Measures

The circumradius *R* ≈ 0.64502 of the great inverted snub icosidodecahedron with unit edge length is the second to smallest positive real root of:

Its volume *V* ≈ 2.71387 is given by the second to smallest positive real root of:

These same polynomials define the circumradii and volumes of the snub dodecahedron, the great snub icosidodecahedron, and the great inverted retrosnub icosidodecahedron.

## Related polyhedra

The great inverted disnub icosidodecahedron is a uniform polyhedron compound composed of the two opposite chiral forms of the great inverted snub icosidodecahedron.

Name | OBSA | Schläfli symbol | CD diagram | Picture |
---|---|---|---|---|

Great stellated dodecahedron | gissid | {5/3,3} | x5/3o3o () | |

Quasitruncated great stellated dodecahedron | quit gissid | t{5/3,3} | x5/3x3o () | |

Great icosidodecahedron | gid | r{3,5/3} | o5/3x3o () | |

Truncated great icosahedron | tiggy | t{3,5/3} | o5/3x3x () | |

Great icosahedron | gike | {3,5/3} | o5/3o3x () | |

Quasirhombicosidodecahedron | qrid | rr{3,5/3} | x5/3o3x () | |

Great quasitruncated icosidodecahedron | gaquatid | tr{3,5/3} | x5/3x3x () | |

Great inverted snub icosidodecahedron | gisid | sr{3,5/3} | s5/3s3s () |

## External links

- Bowers, Jonathan. "Polyhedron Category 6: Snubs" (#70).

- Klitzing, Richard. "gisid".

- Wikipedia Contributors. "Great inverted snub icosidodecahedron".
- McCooey, David. "Great Inverted Snub icosidodecahedron"