# Prohexagonal prismatic symmetry

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Prohexagonal prismatic symmetry | |
---|---|

Rank | 3 |

Space | Spherical |

Order | 12 |

**Prohexagonal prismatic symmetry**, also known as **prohippic symmetry** and notated as **G _{2}+×A_{1}**, is a 3D spherical symmetry group. It is equivalent to the symmetry of a hexagonal prism if the bases are seen as having chiral hexagonal rather than full hexagonal symmetry.

### Subgroups[edit | edit source]

- Chiral hexagonal pyramidal symmetry (maximal)
- Protriangular prismatic symmetry (maximal)
- Protriangular antiprismatic symmetry (maximal)
- Chiral triangular pyramidal symmetry
- Prodigonal prismatic symmetry (maximal)
- 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)