# Digonal prismatic symmetry

(Redirected from K3)

Digonal prismatic symmetry | |
---|---|

Rank | 3 |

Space | Spherical |

Order | 8 |

Info | |

Coxeter diagram | |

Elements | |

Axes | 2 × K_{2}×I |

Related polytopes | |

Omnitruncate | Cuboid |

**Digonal prismatic symmetry**, also known as **brick symmetry** or **cuboidal symmetry** and notated as *K _{3}*, is a 3D spherical Coxeter group. It is the symmetry group of the cuboid or rectangular box, and appears as a subgroup of octahedral and icosahedral symmetries.

### Subgroups[edit | edit source]

- Prodigonal prismatic symmetry (maximal)
- Chiral digonal prismatic symmetry (maximal)
- Rectangular pyramidal symmetry (maximal)
- Chiral digonal pyramidal symmetry
- Inversion symmetry
- Reflection symmetry
- Identity symmetry

### Convex polytopes with K_{3} symmetry[edit | edit source]

- Cuboid (isogonal)/Rhombic tegum (isotopic)