# Second noble octagrammic triacontahedron

(Redirected from Third noble stellation of rhombic triacontahedron)

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Second noble octagrammic triacontahedron | |
---|---|

Rank | 3 |

Type | Noble |

Space | Spherical |

Elements | |

Faces | 30 rectangular-symmetric octagrams |

Edges | 120 |

Vertices | 60 |

Vertex figure | Butterfly |

Measures (edge lengths , ) | |

Edge length ratio | |

Circumradius | |

Related polytopes | |

Army | Srid |

Dual | Third noble faceting of icosidodecahedron |

Convex core | Rhombic triacontahedron |

Abstract & topological properties | |

Flag count | 480 |

Euler characteristic | –30 |

Orientable | No |

Genus | 32 |

Properties | |

Symmetry | H_{3}, order 120 |

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.