# First noble octagrammic triacontahedron

Jump to navigation
Jump to search

First noble octagrammic triacontahedron | |
---|---|

Rank | 3 |

Type | Noble |

Elements | |

Faces | 30 rectangular-symmetric octagrams |

Edges | 60+60 |

Vertices | 60 |

Vertex figure | Butterfly |

Measures (edge lengths , ) | |

Edge length ratio | |

Circumradius | |

Related polytopes | |

Army | Semi-uniform Ti, edge lengths 1 (pentagons) and (between ditrigons) |

Dual | Second noble faceting of icosidodecahedron |

Conjugate | First noble octagrammic triacontahedron |

Convex core | Rhombic triacontahedron |

Abstract & topological properties | |

Flag count | 480 |

Euler characteristic | –30 |

Orientable | No |

Genus | 32 |

Properties | |

Symmetry | H_{3}, order 120 |

Flag orbits | 4 |

Convex | No |

Nature | Tame |

History | |

Discovered by | Max Brückner |

First discovered | 1906 |

The **first noble octagrammic triacontahedron** is a noble polyhedron. Its 30 congruent faces are rectangular-symmetric octagrams meeting at congruent order-4 vertices. It is a faceting of the same semi-uniform truncated icosahedron hull as that of the rhombidodecadodecahedron.

The ratio between the shortest and longest edges is 1: ≈ 1:0.77460.