# Triangular antipodium

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Triangular antipodium | |
---|---|

Rank | 3 |

Notation | |

Bowers style acronym | Trapo |

Coxeter diagram | xo3oy&#z |

Elements | |

Faces | 3+3 isosceles triangles, 1+1 triangles |

Edges | 3+3+6 |

Vertices | 3+3 |

Vertex figure | Isosceles trapezoid (two types) |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Pyramidal-symmetric triangular antitegum |

Abstract & topological properties | |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | A_{2}×I, order 6 |

Convex | Yes |

Nature | Tame |

The **triangular antipodium** or **trapo** is a variant of the triangular antiprism where the bases are different sized equilateral triangles. The version with all equal edges is the regular octahedron, one of the Platonic solids, but other versions exist with isosceles triangles as the sides. In the latter case its Coxeter diagram could be given as xo3oy&#z.

## In vertex figures[edit | edit source]

5 uniform polychora have triangular antipodiums for vertex figures, including the convex small disprismatotesseractihexadecachoron and small disprismatohexacosihecatonicosachoron, as well as the nonconvex small disprismatodishecatonicosachoron, small dishexacosidishecatonicosachoron, and great hexacosihecatonicosidishecatonicosachoron.