# Great inverted pentagonal hexecontahedron

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

Rank | 3 |

Type | Uniform dual |

Notation | |

Coxeter diagram | p5/3p3p |

Elements | |

Faces | 60 mirror-symmetric concave pentagons |

Edges | 30+60+60 |

Vertices | 12+20+60 |

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 |

Conjugates | Pentagonal hexecontahedron, great pentagonal hexecontahedron, great pentagrammic hexecontahedron |

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

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 links[edit | edit source]

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