# Great inverted pentagonal hexecontahedron

The **great inverted pentagonal hexecontahedron** is a uniform dual polyhedron. It consists of 60 mirror-symmetric concave pentagons, each with two short and three long edges.

Great inverted pentagonal hexecontahedron | |
---|---|

Rank | 3 |

Type | Uniform dual |

Space | Spherical |

Notation | |

Coxeter diagram | p5/3p3p |

Elements | |

Faces | 60 mirror-symmetric concave pentagons |

Edges | 30+60+60 |

Vertices | 20+60+12 |

Vertex figure | 20+60 triangles, 12 pentagrams |

Measures (edge length 1) | |

Inradius | ≈ 0.25744 |

Dihedral angle | ≈ 78.35920° |

Central density | 13 |

Related polytopes | |

Dual | 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 |

If its dual, the great inverted snub icosidodecahedron, has unit edge length, then the pentagon faces' short edges have approximate length 0.23186 (equal to a root of the polynomial ), and the long edges have approximate length 0.81801 (equal to a root of the polynomial ).

A dihedral angle can be given as acos(α), where α ≈ 0.20178 is a real root of the polynomial .

The inradius R ≈ 0.25744 of the great inverted pentagonal hexecontahedron with unit edge length is equal to the square root of a real root of .

## External linksEdit

- Wikipedia Contributors. "Great inverted pentagonal hexecontahedron".
- McCooey, David. "Great Inverted Pentagonal Hexecontahedron"