# Crossed isosceles trapezoid

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Crossed isosceles trapezoid | |
---|---|

Rank | 2 |

Notation | |

Bowers style acronym | Crotraz |

Coxeter diagram | x(–x)&#x |

Elements | |

Edges | 1+1+2 |

Vertices | 2+2 |

Vertex figure | Dyad |

Related polytopes | |

Army | Traz |

Dual | Dart |

Conjugate | Crossed isosceles trapezoid |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | A_{1}×I, order 2 |

Convex | No |

Nature | Tame |

The **crossed isosceles trapezoid** is a crossed trapezoid with a single symmetry axis. Equivalently, it is a crossed trapezoid with the same leg lengths and base angles. It has 1 top edge, 2 intersecting side edges of the same length, and 1 base edge. It has 2 pairs of identical vertices, as the angles at either end of the bases are the same.

## In vertex figures[edit | edit source]

The crossed antiprisms have crossed isosceles trapezoids for vertex figures, along with 7 other uniform polyhedra:

Name | Picture | Edge lengths |
---|---|---|

Quasirhombicuboctahedron | 1, √2, √2, √2 | |

Small cubicuboctahedron | 1, √2+√2, √2, √2+√2 | |

Quasirhombicosidodecahedron | 1, √2, (√5–1)/2, √2 | |

Icosidodecadodecahedron | (√5–1)/2, √3, (1+√5)/2, √3 | |

Small dodecicosidodecahedron | 1, √(5+√5)/2, (1+√5)/2, √(5+√5)/2 | |

Great icosicosidodecahedron | 1, √3, (1+√5)/2, √3 | |

Small ditrigonal dodecicosidodecahedron | 1, √(5+√5)/2, (√5–1)/2, √(5+√5)/2 |