# Noble tetragonal tetracontoctahedron

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Noble tetragonal tetracontoctahedron | |
---|---|

Rank | 3 |

Type | Noble |

Space | Spherical |

Elements | |

Faces | 48 irregular tetragons |

Edges | 24+24+48 |

Vertices | 24 |

Vertex figure | Mirror-symmetric octagram |

Number of external pieces | 384 |

Level of complexity | 48 |

Related polytopes | |

Army | Semi-uniform truncated octahedron |

Dual | Noble faceting of great rhombicuboctahedron |

Convex core | Non-Catalan disdyakis dodecahedron |

Abstract & topological properties | |

Flag count | 384 |

Euler characteristic | –24 |

Orientable | Yes |

Genus | 13 |

Properties | |

Symmetry | B_{3}, order 48 |

Convex | No |

Nature | Tame |

The **noble tetragonal tetracontoctahedron** is a noble polyhedron. Its 48 congruent faces are convex irregular quadrilaterals meeting at congruent order-8 vertices. It is a faceting of a semi-uniform truncated octahedral convex hull.

The ratio between the longest and shortest edges is 1:*a* ≈ 1:1.57021, where *a* is the positive real root of .

## Vertex coordinates[edit | edit source]

The vertex coordinates are all permutations of , where is the real root of .