# Hexagonal symmetry

**Hexagonal symmetry**, also known as **higgic symmetry** and notated as **G _{2}**, is a 2D spherical Coxeter group. It is the symmetry group of the hexagon, with 6 rotation and 6 reflection elements.

Hexagonal symmetry | |
---|---|

File:Hexagon with symmetry axes.svg | |

Rank | 2 |

Space | Spherical |

Order | 12 |

Info | |

Coxeter diagram | |

Elements | |

Axes | 6 × A_{1} |

Related polytopes | |

Omnitruncate | Dihexagon |

### Subgroups edit

- Chiral hexagonal symmetry (maximal)
- Triangular symmetry (maximal)
- Chiral triangular symmetry
- Rectangular symmetry (maximal)
- Inversion symmetry
- Reflection symmetry
- Identity symmetry