# Ambotruncatotetrahedral hecatonicosachoron

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Ambotruncatotetrahedral hecatonicosachoron | |
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File:Ambotruncatotetrahedral hecatonicosachoron.png | |

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Matehi |

Elements | |

Cells | 120 truncated tetrahedra, 120 chiral rectified truncated tetrahedra |

Faces | 480 triangles, 720 isosceles triangles, 480 ditrigons |

Edges | 720+1440 |

Vertices | 720 |

Vertex figure | Mirror-symmetric triangular prism |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Notched heptacosicosachoron |

Abstract & topological properties | |

Flag count | 25920 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | A_{3}●H_{3}, order 1440 |

Convex | Yes |

Nature | Tame |

The **ambotruncatotetrahedral hecatonicosachoron** or **matehi** is a convex isogonal polychoron that consists of 120 chiral rectified truncated tetrahedra and 120 truncated tetrahedra. 3 rectified truncated tetrahedra and 2 truncated tetrahedra join at each vertex. However, it cannot be made scaliform.

The ratio between the longest and shortest edges is 1: ≈ 1:1.61803.