# Noble octagonal triacontahedron

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Noble octagonal triacontahedron | |
---|---|

Rank | 3 |

Type | Noble |

Elements | |

Faces | 30 rectangular-symmetric octagons |

Edges | 60+60 |

Vertices | 60 |

Vertex figure | Butterfly |

Measures (edge lengths , ) | |

Edge length ratio | |

Circumradius | |

Related polytopes | |

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

Dual | First noble faceting of icosidodecahedron |

Conjugate | Second 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 **noble octagonal triacontahedron** is a noble polyhedron. Its 30 congruent faces are rectangular-symmetric octagons meeting at congruent order-4 vertices. It is a faceting of the same semi-uniform truncated icosahedron hull as that of the truncated great dodecahedron.

The ratio between the shortest and longest edges is 1: ≈ 1:3.07768.

## Vertex coordinates[edit | edit source]

A noble octagonal triacontahedron, centered at the origin, has vertex coordinates given by all permutations of:

- ,

plus all even permutations of:

- ,
- .

These are the same coordinates as the truncated great dodecahedron.