# Rhombus

The **rhombus**, or **rhomb**, is a quadrilateral with all four edges of the same length. It has two different angles, and its diagonals are always at right angles. It is a special case of a parallelogram.

Rhombus | |
---|---|

Rank | 2 |

Type | Isotopic |

Notation | |

Bowers style acronym | Rhomb |

Coxeter diagram | m2m |

Elements | |

Edges | 4 |

Vertices | 2+2 |

Vertex figure | Dyad |

Measures (edge length 1, angle α) | |

Inradius | |

Area | |

Angles | Acute: |

Obtuse: | |

Height | |

Central density | 1 |

Related polytopes | |

Army | Rhomb |

Regiment | Rhomb |

Dual | Rectangle |

Conjugate | None |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | K_{2}, order 4 |

Convex | Yes |

Nature | Tame |

The two angles of a rhombus add up to 180°, and one is always acute, the other is obtuse. Rhombi occur as faces in two of the Catalan solids, namely the rhombic dodecahedron and rhombic triacontahedron.

A rhombus can be considered to be the tegum product of two dyads of different lengths. These two dyads then form the two diagonals of the rhombus.

## Golden rhombus edit

The **golden rhombus**^{[1]}^{[2]} is a rhombus whose diagonals have the golden ratio. It appears as a face of the golden isozonohedra as well as other polyhedra such as the rhombic hexecontahedron.

### Vertex coordinates edit

The coordinates of a golden rhombus centered at the origin with side lengths equal to 1:

- ,
- .

## References edit

## External links edit

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