# Second noble octagrammic triacontahedron

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Second 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 | Srid |

Dual | Third noble faceting of icosidodecahedron |

Conjugate | Noble octagonal 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 **second 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 a uniform small rhombicosidodecahedron hull.

The ratio between the shortest and longest edges is 1: ≈ 1:1.37638.

## Vertex coordinates[edit | edit source]

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

- ,

along with all even permutations of

- ,
- .

Other noble polyhedra that can have these coordinates are the Crennell number 4 stellation of the icosahedron and the third noble unihexagrammic hexecontahedron.