# Isosceles trapezoidal pyramid

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Isosceles trapezoidal pyramid | |
---|---|

Rank | 3 |

Space | Spherical |

Notation | |

Bowers style acronym | Trapyr |

Coxeter diagram | oxx&#x |

Elements | |

Faces | 1+1 isosceles triangles, 2 scalene triangles, 1 isosceles trapezoid |

Edges | 1+1+2+2+2 |

Vertices | 1+2+2 |

Vertex figure | 1 isosceles trapezoid, 1+1 isosceles triangles, 2 scalene triangles |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Kite pyramid |

Abstract properties | |

Euler characteristic | 2 |

Topological properties | |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | A_{1}×I×I, order 2 |

Convex | Yes |

Nature | Tame |

An **isosceles trapezoidal pyramid** is a pyramid based on an isosceles trapezoid. It has 1 isosceles trapezoid as the base, 2 different isosceles triangles, and 2 identical scalene triangles as faces, with only bilateral symmetry.

## In vertex figures[edit | edit source]

A total of 30 uniform polychora have isosceles trapezoidal pyramids for vertex figures, including all the runcitruncated polychora, also known as prismatorhombates. In addition, 7 prisms, as well as all non-crossed antiprismatic prisms, have isosceles trapezoidal pyramids for vertex figures.