# Rectangular pyramid

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Rectangular pyramid | |
---|---|

Rank | 3 |

Notation | |

Bowers style acronym | Rectpy |

Coxeter diagram | ox oy&#z |

Elements | |

Faces | 2+2 isosceles triangles, 1 rectangle |

Edges | 2+2+4 |

Vertices | 1+4 |

Vertex figures | 1 rectangle |

4 scalene triangles | |

Measures (edge lengths a, b [base], ℓ [lacing]) | |

Circumradius | |

Volume | |

Height | |

Central density | 1 |

Related polytopes | |

Army | Rectpy |

Regiment | Rectpy |

Dual | Rhombic pyramid |

Conjugate | Rectangular pyramid |

Abstract & topological properties | |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | K_{2}×I, order 4 |

Convex | Yes |

Nature | Tame |

The **rectangular pyramid**, or **rectpy**, is a pyramid based on a rectangle. As such it has 1 rectangle base and 2 pairs of isosceles triangles as sides, with 3 types of edges.

## In vertex figures[edit | edit source]

Rectangular pyramids occur as vertex figures in 4 prismatic uniform polychora, the cuboctahedral prism, icosidodecahedral prism, dodecadodecahedral prism, and great icosidodecahedral prism. Although a few other polychora have rectangle-based pyramids as vertex figures, these generally tend to have the symmetry of isosceles trapezoidal pyramids instead.