# Hexagonal prismatic symmetry

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### Convex polytopes with G

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]

- (G
_{2}×A_{1})/2 - (G
_{2}×A_{1})+ - G
_{2}×I - (G
_{2}+×A_{1})/2 - G
_{2}+×A_{1} - G
_{2}+×I - A
_{2}×A_{1} - (A
_{2}×A_{1})+ - A
_{2}×I - A
_{2}+×A_{1} - A
_{2}+×I - K
_{3} - K
_{3}+ - K
_{2}×I - K
_{2}+×A_{1} - K
_{2}+×I - ±(I×I×I)
- A
_{1}×I×I - I×I×I

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

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