# Ditrigon

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Ditrigon | |
---|---|

Rank | 2 |

Type | Semi-uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Dit |

Coxeter diagram | x3y |

Elements | |

Edges | 3+3 |

Vertices | 6 |

Vertex figure | Dyad |

Measures (edge lengths a, b) | |

Circumradius | |

Area | |

Angle | 120° |

Central density | 1 |

Related polytopes | |

Army | Dit |

Dual | Triambus |

Conjugate | Ditrigon |

Abstract properties | |

Flag count | 6+6 |

Net count | 1 |

Euler characteristic | 0 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | A_{2}, order 6 |

Convex | Yes |

Nature | Tame |

The **ditrigon** is a convex semi-uniform hexagon. As such it has 6 sides that alternate between two edge lengths, with each vertex joining one side of each length. All interior angles of a ditrigon measure 120°. If the side lengths are equal, the result is the regular hexagon.

## Vertex Coordinates[edit | edit source]

A ditrigon with edge lengths *a* and *b* has the vertex coordinates

- ,

- ,

- .

For retrograde ditrigons (i.e. Tripods and Propeller tripods), *a* is negative.

## In vertex figures[edit | edit source]

The ditrigon appears as a vertex figure in one uniform polyhedron, namely the small ditrigonary icosidodecahedron. This ditrigon has edge lengths of 1 and (√5–1)/2.

## External links[edit | edit source]

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

- Klitzing, Richard. "Polygons"