# Joined pentachoron

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Joined pentachoron | |
---|---|

Rank | 4 |

Type | Uniform dual |

Space | Spherical |

Notation | |

Bowers style acronym | Jop |

Coxeter diagram | o3m3o3o () |

Elements | |

Cells | 10 triangular tegums |

Faces | 30 isosceles triangles |

Edges | 10+20 |

Vertices | 5+5 |

Vertex figure | 5 tetrahedra, 5 cubes |

Measures (edge length 1) | |

Dichoral angle | |

Central density | 1 |

Related polytopes | |

Army | Jop |

Regiment | Jop |

Dual | Rectified pentachoron |

Abstract & topological properties | |

Flag count | 360 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | A_{4}, order 120 |

Convex | Yes |

Nature | Tame |

The **joined pentachoron** or **jop**, also known as the **triangular-tegmatic decachoron** or **tibbid**, is a convex isochoric polychoron with 10 triangular tegums as cells. It can be obtained as the dual of the rectified pentachoron.

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

The ratio between the longest and shortest edges is 1:1.5. Each face is an isosceles triangle that uses one long and two short edges.

## Isogonal derivatives[edit | edit source]

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

- Triangular tegum (30): Rectified pentachoron
- Isosceles triangle (30): Semi-uniform small rhombated pentachoron
- Edge (10): Rectified pentachoron
- Edge (20): Semi-uniform small prismatodecachoron
- Vertex (5): Pentachoron
- Vertex (5): Pentachoron

## External links[edit | edit source]

- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".

- Klitzing, Richard. "tibbid".

- Quickfur. "The Joined Pentachoron".