# Compound of two great inverted retrosnub icosidodecahedra

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Compound of two great inverted retrosnub icosidodecahedra | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Gidrissid |

Elements | |

Components | 2 great inverted retrosnub icosidodecahedra |

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

Edges | 60+120+120 |

Vertices | 120 |

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

Measures (edge length 1) | |

Circumradius | ≈ 0.58000 |

Volume | ≈ 2.07520 |

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

3–3: ≈ 21.72466° | |

Central density | 74 |

Number of external pieces | 2580 |

Related polytopes | |

Army | Semi-uniform Grid |

Regiment | Gidrissid |

Dual | Compound of two great pentagrammic hexecontahedra |

Conjugates | Compound of two snub dodecahedra, compound of two great snub icosidodecahedra, compound of two great inverted snub icosidodecahedra |

Convex core | Order-6-truncated disdyakis triacontahedron |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

The **great diretrosnub icosidodecahedron**, **gidrissid**, or **compound of two great inverted retrosnub 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 retrosnub icosidodecahedral antiprism, which is four-dimensional.

## Measures[edit | edit source]

The circumradius of the great diretrosnub icosidodecahedron with unit edge length is the smallest positive real root of:

Its volume is given by the smallest positive real root of:

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category C10: Disnubs" (#75).

- Klitzing, Richard. "gidrissid".

- Wikipedia Contributors. "Compound of two great retrosnub icosidodecahedra".