# Pentagonal icositetrahedron

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Pentagonal icositetrahedron | |
---|---|

Rank | 3 |

Type | Uniform dual |

Space | Spherical |

Notation | |

Bowers style acronym | Pedid |

Coxeter diagram | p4p3p () |

Elements | |

Faces | 24 floret pentagons |

Edges | 12+24+24 |

Vertices | 6+8+24 |

Vertex figure | 6 squares, 8+24 triangles |

Measures (edge length 1) | |

Dihedral angle | ≈ 136.30923° |

Central density | 1 |

Number of external pieces | 24 |

Level of complexity | 10 |

Related polytopes | |

Army | Pedid |

Regiment | Pedid |

Dual | Snub cube |

Conjugate | Pentagonal icositetrahedron |

Abstract & topological properties | |

Flag count | 240 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | B_{3}+, order 24 |

Convex | Yes |

Nature | Tame |

The **pentagonal icositetrahedron**, also called the **petaloid disdodecahedron** or **pedid**, is one of the 13 Catalan solids. It has 24 floret pentagons as faces, with 6 order-4 and 8+24 order-3 vertices. It is the dual of the uniform snub cube.

Each face of this polyhedron is an irregular pentagon with 3 short and 2 long edges. The long edges are around 1.41964 times the length of the shorter ones. Each face has one angle (between two long edges) measuring around 80.75170°, while its other four angles measure around 114.81207°.

## External links[edit | edit source]

- Wikipedia Contributors. "Pentagonal icositetrahedron".
- McCooey, David. "Pentagonal Icositetrahedron"