# First noble kipiscoidal hecatonicosahedron

The **first noble kipiscoidal hecatonicosahedron** is a noble polyhedron. Its 120 congruent faces are asymmetric pentagons that meet at congruent order-5 vertices. It is a faceting of a non-uniform great rhombicosidodecahedral convex hull.

First noble kipiscoidal hecatonicosahedron | |
---|---|

Rank | 3 |

Type | Noble |

Elements | |

Faces | 120 asymmetric pentagons |

Edges | 60+120+120 |

Vertices | 120 |

Vertex figure | Asymmetric pentagon |

Measures (edge lengths ≈0.51029, ≈0.93956, ≈1.29954) | |

Edge length ratio | ≈2.54667 |

Circumradius | 1 |

Related polytopes | |

Army | Non-uniform Grid, edge lengths ≈0.22676 (between rectangle and ditrigon), ≈0.19060 (between rectangle and dipentagon), ≈0.34364 (between ditrigon and dipentagon) |

Dual | Second noble kipiscoidal hecatonicosahedron |

Convex core | Non-Catalan disdyakis triacontahedron |

Abstract & topological properties | |

Flag count | 1200 |

Euler characteristic | –120 |

Orientable | No |

Genus | 122 |

Properties | |

Symmetry | H_{3}, order 120 |

Flag orbits | 10 |

Convex | No |

Nature | Tame |

The ratio between the shortest and longest edges is approximately 1:2.54667.