# Second noble triangular hecatonicosahedron

(Redirected from Fifth noble faceting of icosidodecahedron)

Second noble triangular hecatonicosahedron | |
---|---|

Rank | 3 |

Type | Noble |

Elements | |

Faces | 120 scalene triangles |

Edges | 60+60+60 |

Vertices | 30 |

Vertex figure | Rectangular-symmetric dodecagram |

Measures (edge lengths , , ) | |

Circumradius | |

Number of external pieces | 720 |

Level of complexity | 40 |

Related polytopes | |

Army | Id |

Dual | Fifth noble stellation of rhombic triacontahedron |

Conjugate | First noble triangular hecatonicosahedron |

Convex core | Disdyakis 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 **second noble triangular hecatonicosahedron** is a noble polyhedron. Its 120 congruent faces are scalene triangles meeting at congruent order-12 vertices. It is a faceting of a uniform icosidodecahedron hull.

The ratio between the shortest and longest edges is 1: ≈ 1:1.47337.

The triangular faces are similar to the vertex figure of the great quasitruncated icosidodecahedron.

## Vertex coordinates[edit | edit source]

Its vertices are the same as those of an icosidodecahedron.