# Medial inverted pentagonal hexecontahedron

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Medial inverted pentagonal hexecontahedron | |
---|---|

Rank | 3 |

Type | Uniform dual |

Space | Spherical |

Notation | |

Coxeter diagram | p5/3p5p () |

Elements | |

Faces | 60 irregular pentagons |

Edges | 60+60+30 |

Vertices | 60+12+12 |

Vertex figure | 60 triangles, 12 pentagons, 12 pentagrams |

Measures (edge length 1) | |

Inradius | ≈ 0.55808 |

Dihedral angle | ≈ 108.09572° |

Central density | 9 |

Number of pieces | 60 |

Related polytopes | |

Dual | Inverted snub dodecadodecahedron |

Abstract properties | |

Flag count | 600 |

Euler characteristic | –6 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | H_{3}+, order 60 |

Convex | No |

Nature | Tame |

The **medial inverted pentagonal hexecontahedron** is a uniform dual polyhedron. It consists of 60 irregular pentagons, each with two short, one medium, and two long edges. Its dual is the inverted snub dodecadodecahedron.

If the pentagon faces have medium edge length 2, then the short edge length is , and the long edge length is , where is the largest (least negative) real root of the polynomial . The pentagons have three interior angles of , one of , and one of , where is the golden ratio.

A dihedral angle can be given as .

The inradius R ≈ 0.55808 of the medial 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. "Medial inverted pentagonal hexecontahedron".
- McCooey, David. "Medial Inverted Pentagonal Hexecontahedron"