# Chiral cubic symmetry

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### Convex polytopes with BC

Chiral cubic symmetry | |
---|---|

Rank | 3 |

Space | Spherical |

Order | 24 |

Info | |

Coxeter diagram | |

Elements | |

Axes | 3 × (BC_{2}×A_{1})+, 4 × (A_{2})+, 6 × K_{3+} |

**Chiral cubic symmetry**, also known as **chiral octahedral symmetry**, **kicubic symmetry**, or notated as **B _{3}+** or

**BC**, is a 3D spherical symmetry group. It is the symmetry group of the snub cube, or equivalently the symmetry group of the cube or octahedron with all the reflections removed.

_{3}+### Subgroups[edit | edit source]

- A
_{3}+ (maximal) - (B
_{2}×A_{1})+ (maximal) - B
_{2}+×I - (A
_{2}×A_{1})+ (maximal) - A
_{2}+×I - K
_{3}+ - K
_{2}+×I - I×I×I

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

- Cube (regular)/Octahedron (regular)
- Cuboctahedron (isogonal)/Rhombic dodecahedron (isotopic)
- Truncated cube (isogonal)/Triakis octahedron (isotopic)
- Truncated octahedron (isogonal)/Tetrakis hexahedron (isotopic)
- Small rhombicuboctahedron (isogonal)/Deltoidal icositetrahedron (isotopic)
- Snub cube (isogonal)/Pentagonal icositetrahedron (isotopic)