# Triangular pyramid

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Triangular pyramid | |
---|---|

Rank | 3 |

Space | Spherical |

Notation | |

Bowers style acronym | Tripy |

Coxeter diagram | ox3oo&#y |

Elements | |

Faces | 1 equilateral triangle, 3 isosceles triangles |

Edges | 3+3 |

Vertices | 1+3 |

Vertex figures | 1 triangle |

3 isosceles triangles | |

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

Circumradius | |

Volume | |

Height | |

Central density | 1 |

Related polytopes | |

Army | Tripy |

Regiment | Tripy |

Dual | Triangular pyramid |

Conjugate | Triangular pyramid |

Abstract & topological properties | |

Flag count | 24 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | A_{2}×I, order 6 |

Convex | Yes |

Net count | 4 |

Nature | Tame |

The **triangular pyramid**, or **tripy**, is a type of tetrahedron with 1 equilateral triangle as a base and 3 isosceles triangles as sides. It is a pyramid based on the equilateral triangle.

It generally has 2 edge sizes, the base and side edges.

## In vertex figures[edit | edit source]

Triangular pyramids occur as the vertex figures in 8 nonprismatic uniform polychora (including the truncated pentachoron, truncated tesseract, truncated icositetrachoron, truncated hecatonicosachoron, truncated great grand hecatonicosachoron, quasitruncated tesseract, quasitruncated small stellated hecatonicosachoron, and quasitruncated great grand stellated hecatonicosachoron) and 3 polyhedral prisms (the tetrahedral prism, dodecahedral prism, and great stellated dodecahedral prism).