# Triangular prismatic symmetry

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Triangular prismatic symmetry | |
---|---|

Rank | 3 |

Space | Spherical |

Order | 12 |

Info | |

Coxeter diagram | |

Elements | |

Axes | 1 × A_{2}×A_{1}, 3 × K_{2}×I |

Related polytopes | |

Omnitruncate | Ditrigonal prism |

**Triangular prismatic symmetry**, also known as **trippic symmetry** and notated as **A _{2}×A_{1}**, is a 3D spherical Coxeter group. It is the symmetry group of the triangular prism.

### Subgroups[edit | edit source]

- Protriangular prismatic symmetry (maximal)
- Chiral triangular prismatic symmetry (miaxmal)
- Triangular pyramidal symmetry (maximal)
- Chiral triangular pyramidal symmetry
- Rectangular pyramidal symmetry (maximal)
- Chiral digonal pyramidal symmetry
- Reflection symmetry
- Identity symmetry

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

- Triangular prism (isogonal)/Triangular tegum (isotopic)
- Ditrigonal prism (isogonal)/Triambic tegum (isotopic)