# Wedge

Wedge | |
---|---|

Rank | 3 |

Space | Spherical |

Notation | |

Bowers style acronym | Wedge |

Coxeter diagram | ox xx&#y |

Elements | |

Faces | 2 isosceles triangles, 2 isosceles trapezoids, 1 rectangle |

Edges | 1+2+2+4 |

Vertices | 2+4 |

Vertex figures | 2 isosceles triangles |

4 scalene triangles | |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Army | Wedge |

Regiment | Wedge |

Dual | Notch |

Conjugate | Wedge |

Abstract & topological properties | |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | K_{2}×I, order 4 |

Convex | Yes |

Nature | Tame |

The **wedge** is a variant of the triangular prism with a base rectangle, opposite a top edge, with two isosceles triangles and two isosceles trapezoids as faces.

The term "wedge" can also be used generally to refer to any monostratic polytope with a sub-dimensional top base that is not a pyramid.

## In vertex figures[edit | edit source]

Variants of the wedge (with lateral edge lengths of √2) by changing the edge opposite of the square appear as the vertex figure of the uniform small rhombated pentachoron. With a top edge length of √2, it is the vertex figure of the uniform small rhombated tesseract, and with a top edge length of (1+√5)/2, it is the vertex figure of the uniform small rhombated hecatonicosachoron. By changing the base edges perpendicular to the top edge instead, it appears as the vertex figure of the uniform small rhombated hexacosichoron.

Variants of the wedge by changing the two edges parallel to the top edge appear as the vertex figure of the nonuniform rectified decachoron, with edge lengths of √3 for the aforementioned edges, and the nonuniform rectified tetracontoctachoron, with edge lengths of √2+√2 for the aforementioned edges, with both having no corealmic realization.

Including nonconvex cases, the wedge appears as a vertex figure of a total of 23 uniform polychora, commonly known as the **sphenovert** polychora.

Variants of the wedge (with base-parallel edge lengths of √2) by changing the edge opposite to the square appear as the vertex figure of the nonuniform rectified n-gonal duoprisms, and has no corealmic realization.