# Joined icositetrachoron

Joined icositetrachoron | |
---|---|

Rank | 4 |

Type | Uniform dual |

Space | Spherical |

Notation | |

Bowers style acronym | Jico |

Coxeter diagram | o3m4o3o () |

Elements | |

Cells | 96 triangular tegums |

Faces | 288 isosceles triangles |

Edges | 96+144 |

Vertices | 24+24 |

Vertex figure | 24 octahedra, 24 rhombic dodecahedra |

Measures (edge length 1) | |

Dichoral angle | |

Central density | 1 |

Related polytopes | |

Army | Jico |

Regiment | Jico |

Dual | Rectified icositetrachoron |

Abstract & topological properties | |

Flag count | 3456 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | F_{4}, order 1152 |

Convex | Yes |

Nature | Tame |

The **joined icositetrachoron** or **jico**, also known as the **triangular-tegmatic enneacontahexachoron** or **tabene**, is a convex isochoric polychoron with 96 triangular tegums as cells. It can be obtained as the dual of the rectified icositetrachoron.

It can also be obtained as the convex hull of 2 dually-oriented icositetrachora, where one has edge length times that of the other.

The ratio between the longest and shortest edges is 1: ≈ 1:1.34164. Each face is an isosceles triangle that uses one long and two short edges.

## Variations[edit | edit source]

The joined icositetrachoron has variants that remain isochoric under B_{4} symmetry (called the great notched enneacontahexachoron) and D_{4} symmetry (called the skewed notched enneacontahexachoron).

## Isogonal derivatives[edit | edit source]

Substitution by vertices of these following elements will produce these convex isogonal polychora:

- Triangular tegum (96): Rectified icositetrachoron
- Isosceles triangle (288): Small rhombated icositetrachoron
- Edge (96): Rectified icositetrachoron
- Edge (144): Semi-uniform small prismatotetracontoctachoron
- Vertex (24): Icositetrachoron
- Vertex (24): Icositetrachoron

## External links[edit | edit source]

- Klitzing, Richard. "jico".