# Isosceles trapezoid

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Isosceles trapezoid | |
---|---|

Rank | 2 |

Space | Spherical |

Notation | |

Bowers style acronym | Traz |

Coxeter diagram | xy&#z |

Elements | |

Edges | 1+1+2 |

Vertices | 2+2 |

Vertex figure | Dyad |

Measures (edge lengths (small base), (large base), ℓ (lacing)) | |

Area | |

Height | |

Central density | 1 |

Related polytopes | |

Army | Traz |

Dual | Kite |

Conjugate | Isosceles trapezoid |

Abstract properties | |

Euler characteristic | 0 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | A_{1}×I, order 2 |

Convex | Yes |

Nature | Tame |

The **isosceles trapezoid** is a trapezoid with a single symmetry axis. Equivalently, it is a trapezoid with the same leg lengths and base angles. It has 1 top edge, 2 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.

If the legs intersect, the figure may more precisely be called a crossed isosceles trapezoid.

## In vertex figures[edit | edit source]

Every polygonal antiprism has an isosceles trapezoid as its vertex figure. The vertex figures for the crossed antiprisms are themselves crossed, and thus crossed isosceles trapezoids. Seven other uniform polyhedra have trapezoidal vertex figures.

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

Triangular antiprism | 1, 1, 1, 1 | |

Square antiprism | 1, 1, 1, √2 | |

Pentagonal antiprism | 1, 1, 1, (√5+1)/2 | |

Pentagrammic antiprism | 1, 1, 1, (√5–1)/2 | |

Hexagonal antiprism | 1, 1, 1, √3 | |

... | ||

Small rhombicuboctahedron | 1, √2, √2, √2 | |

Great cubicuboctahedron | 1, √2-√2, √2, √2-√2 | |

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

Great dodecicosidodecahedron | 1, √(5-√5)/2, (√5-1)/2, √(5-√5)/2 | |

Rhombidodecadodecahedron | (√5-1)/2, √2, (1+√5)/2, √2 | |

Small icosicosidodecahedron | 1, √3, (√5-1)/2, √3 | |

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