# Irregular tetrahedron

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Irregular tetrahedron | |
---|---|

Rank | 3 |

Notation | |

Bowers style acronym | Irtet |

Coxeter diagram | oooo&#x |

Elements | |

Faces | 1+1+1+1 scalene triangles |

Edges | 1+1+1+1+1+1 |

Vertices | 1+1+1+1 |

Vertex figure | 1+1+1+1 scalene triangles |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Army | Irtet |

Regiment | Irtet |

Dual | Irregular tetrahedron |

Conjugate | Irregular tetrahedron |

Abstract & topological properties | |

Flag count | 24 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | I×I×I, order 1 |

Flag orbits | 24 |

Convex | Yes |

Nature | Tame |

An **irregular tetrahedron** is a tetrahedron with no symmetries. Generally, though not necessarily, it has four different scalene triangles for faces.

## In vertex figures[edit | edit source]

A total of 17 uniform polychora, including the convex great disprismatotesseractihexadecachoron and great disprismatohexacosihecatonicosachoron, have irregular tetrahedra for vertex figures. These are known as omnitruncates or maximized polychora and have the most vertices possible to be uniform in their symmetry.