# Rectangle

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Rectangle | |
---|---|

Rank | 2 |

Type | Semi-uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Rect |

Coxeter diagram | x y |

Elements | |

Edges | 2+2 |

Vertices | 4 |

Vertex figure | Dyad |

Measures (edge lengths a, b) | |

Circumradius | |

Area | |

Angle | 90° |

Central density | 1 |

Related polytopes | |

Army | Rect |

Dual | Rhombus |

Conjugate | Rectangle |

Abstract properties | |

Euler characteristic | 0 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | K_{2}, order 4 |

Convex | Yes |

Nature | Tame |

The **rectangle** is a semi-uniform quadrilateral with 2 pairs of opposite parallel sides. All interior angles of a rectangle measure 90°. A rectangle is the prism product of two dyads of different lengths.

Any rectangle can tile the euclidean plane, regardless of its sides.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a rectangle with side lengths *a* and *b*, centered at the origin, are:

- (±
*a*/2, ±*b*/2).

## In vertex figures[edit | edit source]

Because the rectangle is a semi-uniform polygon, all polyhedra with rectangular vertex figures are quasiregular. They are also all the result of rectification of regular polyhedra.

Name | Picture | Edge lengths |
---|---|---|

Tetratetrahedron | 1, 1 | |

Cuboctahedron | 1, √2 | |

Icosidodecahedron | 1, (1+√5)/2 | |

Great icosidodecahedron | 1, (√5–1)/2 | |

Dodecadodecahedron | (1+√5)/2, (√5–1)/2 |

## External links[edit | edit source]

- Bowers, Jonathan. "Regular Polygons and Other Two Dimensional Shapes".

- Klitzing, Richard. "Polygons"