# Dodecagonal symmetry

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Dodecagonal symmetry | |
---|---|

Rank | 2 |

Space | Spherical |

Order | 24 |

Info | |

Coxeter diagram | |

Elements | |

Axes | 12 × A_{1} |

Related polytopes | |

Omnitruncate | Didodecagon |

**Dodecagonal symmetry**, also known as **doggic symmetry** and notated as **I _{2}(12)**, is a 2D spherical Coxeter group. It is the symmetry group of the dodecagon, with 12 rotation and 12 reflection elements.

### Subgroups[edit | edit source]

- Chiral dodecagonal symmetry (maximal)
- Hexagonal symmetry (maximal)
- Chiral hexagonal symmetry
- Square symmetry (maximal)
- Chiral square symmetry
- Triangular symmetry
- Chiral triangular symmetry
- Rectangular symmetry
- Inversion symmetry
- Reflection symmetry
- Identity symmetry

### Convex polytopes with I_{2}(12) symmetry[edit | edit source]

- Dodecagon (regular)
- Didodecagon (isogonal)/Dodecambus (isotopic)