# Hexagonal prismatic symmetry

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

Rank | 3 |

Space | Spherical |

Order | 24 |

Info | |

Coxeter diagram | |

Elements | |

Axes | 1 × G_{2}×A_{1}, 6 × K_{2}×I |

Related polytopes | |

Omnitruncate | Dihexagonal prism |

**Hexagonal prismatic symmetry**, also known as **hippic symmetry** and notated as **G _{2}×A_{1}**, is a 3D spherical Coxeter group. It is the symmetry group of the hexagonal prism.

### Subgroups[edit | edit source]

- Prohexagonal prismatic symmetry (maximal)
- Chiral hexagonal prismatic symmetry (maximal)
- Hexagonal pyramidal symmetry (maximal)
- Chiral hexagonal pyramidal symmetry
- Triangular prismatic symmetry (maximal)
- Protriangular prismatic symmetry
- Triangular antiprismatic symmetry (maximal)
- Protriangular antiprismatic symmetry
- Chiral triangular prismatic symmetry
- Triangular pyramidal symmetry
- Chiral triangular pyramidal symmetry
- Digonal prismatic symmetry (maximal)
- Prodigonal prismatic symmetry
- Chiral digonal prismatic symmetry
- Rectangular pyramidal symmetry
- Chiral digonal pyramidal symmetry
- Inversion symmetry
- Reflection symmetry
- Identity symmetry

### Convex polytopes with G_{2}×A_{1} symmetry[edit | edit source]

- Hexagonal prism (isogonal)/Hexagonal tegum (isotopic)
- Dihexagonal prism (isogonal)/Hexambic tegum (isotopic)