# First noble kipiscoidal icositetrahedron

The **noble faceting of the snub cube**, or the **first** **noble kipiscoidal icositetrahedron**, is a self-dual noble polyhedron. Its 24 congruent faces are irregular pentagons meeting at congruent order-5 vertices.

First noble kipiscoidal icositetrahedron | |
---|---|

Rank | 3 |

Type | Noble |

Elements | |

Faces | 24 irregular pentagons |

Edges | 12+24+24 |

Vertices | 24 |

Vertex figure | Irregular pentagon |

Number of external pieces | 72 |

Level of complexity | 22 |

Related polytopes | |

Army | Snub cube |

Dual | First noble kipiscoidal icositetrahedron |

Convex core | Pentagonal icositetrahedron |

Abstract & topological properties | |

Flag count | 240 |

Euler characteristic | –12 |

Orientable | Yes |

Genus | 7 |

Properties | |

Symmetry | B_{3}+, order 24 |

Flag orbits | 10 |

Convex | No |

Nature | Tame |

The ratio between the longest and shortest edges is 1:*a* ≈ 1:1.68502, where *a* is the positive real root of a^{6}-4a^{4}+4a^{2}-2.

This was the first noble polyhedron discovered in more than 100 years since Max Brückner studied such figures, by Robert Webb.

## Bibliography edit

- Webb, Robert (2008). "Noble Faceting of Snub Cube".
*Stella*.