# Icositetrachoric symmetry

**Icositetrachoric symmetry**, also known as **icoic symmetry** and notated as **F _{4}**, is a 4D spherical Coxeter group. It is the symmetry group of the regular icositetrachoron.

Icositetrachoric symmetry | |
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Rank | 4 |

Space | Spherical |

Order | 1152 |

Info | |

Coxeter diagram | |

Elements | |

Axes | 24+24 B3 96+96 A2×A1 |

Related polytopes | |

Omnitruncate | Great disprismatoicositetricositetrachoron |

### Subgroups edit

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### Convex polytopes with F_{4} symmetry
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- Icositetrachoron (regular)
- Rectified icositetrachoron (isogonal)/Joined icositetrachoron (isotopic)
- Truncated icositetrachoron (isogonal)/Octakis icositetrachoron (isotopic)
- Icositetricositetrachoron (isogonal)/Disphenoidal diacosioctacontoctachoron (isotopic)
- Small rhombated icositetrachoron (isogonal)/Notched diacosioctacontoctachoron (isotopic)
- Great rhombated icositetrachoron (isogonal)/Sphenoidal pentacosiheptacontahexachoron (isotopic)
- Small disprismatoicositetricositetrachoron (isogonal)/Square-antitegmatic hecatontetracontatetrachoron (isotopic)
- Prismatorhombated icositetrachoron (isogonal)/Deltopyramidal pentacosiheptacontahexachoron (isotopic)
- Great disprismatoicositetricositetrachoron (isogonal)/Tetrahedral chiliahecatonpentacontadichoron (isotopic)

## External links edit

- Wikipedia contributors. "F
_{4}(mathematics)".