# Sphenoid

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Sphenoid | |
---|---|

Rank | 3 |

Notation | |

Coxeter diagram | oox&#x |

Elements | |

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

Edges | 1+1+2+2 |

Vertices | 1+1+2 |

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

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Army | Sphenoid |

Regiment | Sphenoid |

Dual | Sphenoid |

Conjugate | Sphenoid |

Abstract & topological properties | |

Flag count | 24 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | A_{1}×I×I, order 2 |

Flag orbits | 12 |

Convex | Yes |

Nature | Tame |

A **sphenoid** is a type of tetrahedron with only one symmetry axis. As such it has two different isosceles triangles and two identical scalene triangles as faces, and can also be called a **mirror-symmetric tetrahedron**.

## In vertex figures[edit | edit source]

Sphenoids occur as vertex figures in a total of 23 non-prismatic uniform polychora, including all the cantitruncated polychora, also known as great rhombates. They also appear as vertex figures in the prisms of the 10 3D truncates.