# Great pentagonal hexecontahedron

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

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

Rank | 3 |

Type | Uniform dual |

Space | Spherical |

Notation | |

Coxeter diagram | p5/2p3p |

Elements | |

Faces | 60 mirror-symmetric pentagons |

Edges | 30+60+60 |

Vertices | 20+60+12 |

Vertex figure | 20+60 triangles, 12 pentagrams |

Measures (edge length 1) | |

Inradius | ≈ 0.50974 |

Dihedral angle | ≈ 104.43227° |

Central density | 7 |

Related polytopes | |

Dual | Great 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 snub icosidodecahedron, has unit edge length, then the pentagon faces' short edges have approximate length 0.49069 (equal to a root of the polynomial ), and the long edges have approximate length 0.64563 (equal to a root of the polynomial ). The hexagons have four interior angles of , and one of , where is the negative root of the polynomial , and is the golden ratio.

A dihedral angle can be given as .

The inradius R ≈ 0.50974 of the great pentagonal hexecontahedron with unit edge length is equal to the square root of a real root of .

## External linksEdit

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