# Final stellation of the rhombic triacontahedron

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Final stellation of the rhombic triacontahedron | |
---|---|

Rank | 3 |

Type | Noble |

Elements | |

Faces | 30 rectangular-symmetric dodecagrams |

Edges | 60+60+60 |

Vertices | 120 |

Vertex figure | Scalene triangle, edge lengths ~1.83181532266 ~2.139581850425 ~1.61249720186 |

Number of external pieces | 240 |

Level of complexity | 20 |

Related polytopes | |

Army | Grid |

Dual | First noble triangular hecatonicosahedron |

Conjugate | Fifth noble stellation of rhombic triacontahedron |

Convex core | Rhombic triacontahedron |

Abstract & topological properties | |

Flag count | 720 |

Euler characteristic | –30 |

Orientable | Yes |

Genus | 16 |

Properties | |

Symmetry | H_{3}, order 120 |

Flag orbits | 6 |

Convex | No |

Nature | Tame |

History | |

Discovered by | Edmond Hess |

First discovered | 1876 |

The **final stellation of the rhombic triacontahedron** is a noble polyhedron that is a faceting of the uniform great rhombicosidodecahedron. It has 30 rectangular-symmetric dodecagrammic faces.

The ratio between the longest and shortest edges is 1: ≈ 1:1.08576.