# Pentagonal hexecontahedron

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Pentagonal hexecontahedron | |
---|---|

Rank | 3 |

Type | Uniform dual |

Space | Spherical |

Notation | |

Bowers style acronym | Sapedit |

Coxeter diagram | p5p3p () |

Elements | |

Faces | 60 floret pentagons |

Edges | 30+60+60 |

Vertices | 12+20+60 |

Vertex figure | 12 pentagons, 20+60 triangles |

Measures (edge length 1) | |

Dihedral angle | ≈ 153.17873° |

Central density | 1 |

Related polytopes | |

Army | Sapedit |

Regiment | Sapedit |

Dual | Snub dodecahedron |

Conjugates | Great pentagonal hexecontahedron, great inverted pentagonal hexecontahedron, great pentagrammic hexecontahedron |

Abstract & topological properties | |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | H_{3}+, order 60 |

Convex | Yes |

Nature | Tame |

The **pentagonal hexecontahedron**, also called the **small petaloid ditriacontahedron**, is one of the 13 Catalan solids. It has 60 floret pentagons as faces, with 12 order-5 and 20+60 order-3 vertices. It is the dual of the uniform snub dodecahedron.

Each face of this polyhedron is an irregular pentagon with 3 short and 2 long edges. The long edges are around 1.74985 times the length of the shorter ones. Each face has one angle (between two long edges) measuring around 67.45351°, while its other four angles measure around 118.13662°.

## External links[edit | edit source]

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