# Notched triacontachoron

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Notched triacontachoron | |
---|---|

Rank | 4 |

Type | Uniform dual |

Notation | |

Coxeter diagram | m3o3m3o () |

Elements | |

Cells | 30 notches |

Faces | 30 isosceles triangles, 60 scalene triangles |

Edges | 10+20+20+30 |

Vertices | 5+5+10 |

Vertex figure | 10 triangular bipyramids, 5 cubes, 5 rhombic dodecahedra |

Measures (edge length 1) | |

Dichoral angle | |

Central density | 1 |

Related polytopes | |

Dual | Small rhombated pentachoron |

Abstract & topological properties | |

Flag count | 1080 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | A_{4}, order 120 |

Convex | Yes |

Nature | Tame |

The **notched triacontachoron** is a convex isochoric polychoron with 30 notches as cells. It can be obtained as the dual of the small rhombated pentachoron.

It can also be constructed as the convex hull of 2 dual pentachora and a rectified pentachoron. If the smaller pentachoron has edge length 1, the larger pentachoron has edge length and the rectified pentachoron has edge length .

The ratio between the longest and shortest edges is 1: = 1:2.625.

## External links[edit | edit source]

- Klitzing, Richard. "dusrip".