# Noble enneagrammic icosahedron

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Noble enneagrammic icosahedron | |
---|---|

Rank | 3 |

Type | Noble |

Elements | |

Faces | 20 triangular-symmetric enneagrams |

Edges | 30+60 |

Vertices | 60 |

Vertex figure | Isosceles triangle |

Measures (edge lengths , ) | |

Edge length ratio | |

Circumradius | |

Central density | 5 |

Number of external pieces | 180 |

Level of complexity | 10 |

Related polytopes | |

Army | Small rhombicosidodecahedron |

Dual | Small noble triangular hexecontahedron |

Conjugate | Final stellation of the icosahedron |

Convex core | Icosahedron |

Abstract & topological properties | |

Flag count | 360 |

Euler characteristic | –10 |

Orientable | Yes |

Genus | 6 |

Properties | |

Symmetry | H_{3}, order 120 |

Flag orbits | 3 |

Convex | No |

Nature | Tame |

History | |

Discovered by | Edmond Hess |

First discovered | 1875 |

The **noble enneagrammic icosahedron** or **Crennell number 4 stellation of the icosahedron** is the conjugate to the final stellation of the icosahedron. It is a noble polyhedron with 20 triangular-symmetric enneagrams for faces. Its convex hull is the uniform small rhombicosidodecahedron.