# Triangular antitegum

(Redirected from Triangular trapezohedron)

Triangular antitegum | |
---|---|

Rank | 3 |

Type | Isotopic |

Notation | |

Bowers style acronym | Trate |

Coxeter diagram | p2p6o () |

Elements | |

Faces | 6 rhombi |

Edges | 6+6 |

Vertices | 2+6 |

Vertex figure | 6 isosceles triangles, 2 triangles |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Army | Trate |

Regiment | Trate |

Dual | Triangular antiprism |

Conjugate | Triangular antitegum |

Abstract & topological properties | |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | (G_{2}×A_{1})/2, order 12 |

Convex | Yes |

Nature | Tame |

The **triangular antitegum**, also known as the **trigonal trapezohedron**, is an antitegum based on a triangle. If all angles are equal, the result is the regular cube. The general triangular antitegum has 6 identical rhombic faces.

Variants of the triangular antitegum exist that are dual to the triangular antipodium as well, using 2 different sets of 3 kites for faces.