# Great inverted retrosnub icosidodecahedron

Great inverted retrosnub icosidodecahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Girsid |

Coxeter diagram | s5/3s3/2s () |

Elements | |

Faces | 20+60 triangles, 12 pentagrams |

Edges | 30+60+60 |

Vertices | 60 |

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

Measures (edge length 1) | |

Circumradius | ≈ 0.58000 |

Volume | ≈ 1.03760 |

Dihedral angles | 5/2–3: ≈ 67.31029° |

3–3: ≈ 21.72466° | |

Central density | 37 |

Number of external pieces | 1800 |

Level of complexity | 139 |

Related polytopes | |

Army | Non-uniform Snid |

Regiment | Girsid |

Dual | Great pentagrammic hexecontahedron |

Conjugates | Snub dodecahedron, great snub icosidodecahedron, great inverted snub icosidodecahedron |

Abstract & topological properties | |

Flag count | 600 |

Euler characteristic | 2 |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | H_{3}+, order 60 |

Convex | No |

Nature | Tame |

The **great inverted retrosnub icosidodecahedron** or **girsid**, also called the **great retrosnub icosidodecahedron**, 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.

## Measures[edit | edit source]

The circumradius *R* ≈ 0.58000 of the great inverted retrosnub icosidodecahedron with unit edge length is the smallest positive real root of:

Its volume *V* ≈ 1.03760 is given by the 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 snub icosidodecahedron.

## Related polyhedra[edit | edit source]

The great diretrosnub icosidodecahedron is a uniform polyhedron compound composed of the 2 opposite chiral forms of the great inverted retrosnub icosidodecahedron.

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category 6: Snubs" (#73).

- Klitzing, Richard. "girsid".

- Wikipedia Contributors. "Great retrosnub icosidodecahedron".
- McCooey, David. "Great Retrosnub Icosidodecahedron"