# Joined hexadecachoron

Joined hexadecachoron | |
---|---|

Rank | 4 |

Type | Uniform dual |

Notation | |

Coxeter diagram | o4m3o3o () |

Elements | |

Cells | 32 triangular tegums |

Faces | 96 isosceles triangles |

Edges | 24+64 |

Vertices | 8+16 |

Vertex figure | 16 tetrahedra, 8 rhombic dodecahedra |

Measures (edge length 1) | |

Dichoral angle | |

Central density | 1 |

Related polytopes | |

Dual | Rectified tesseract |

Abstract & topological properties | |

Flag count | 1152 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{4}, order 384 |

Convex | Yes |

Nature | Tame |

The **joined hexadecachoron**, **joined square duotegum**, or **transitional digonal double tegmotrapezohedroid**, also known as the **triangular-tegmatic triacontadichoron** or **tibbit**, is a convex isochoric polychoron with 32 triangular tegums as cells. It can be obtained as the dual of the rectified tesseract.

As the joined square duotegum, it is the square member of an infinite family of isochoric joined duotegums.

It can also be obtained as the convex hull of a tesseract and a hexadecachoron, where the edges of the hexadecachoron are times the length of those of the tesseract.

The ratio between the longest and shortest edges is 1: ≈ 1:1.60357. Each face is an isosceles triangle that uses one long and two short edges.

## Variations[edit | edit source]

The joined hexadecachoron has a variant with D_{4} symmetry that remains isochoric. In this variant the tegums become apiculated triangular pyramids, and the variant could be called an apiculatotripyramidal triacontadichoron.

## Isogonal derivatives[edit | edit source]

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

- Triangular tegum (32): Rectified icositetrachoron
- Isosceles triangle (96): Semi-uniform small rhombated tesseract
- Edge (24): Icositetrachoron
- Edge (64): Semi-uniform small disprismatotesseractihexadecachoron
- Vertex (8): Hexadecachoron
- Vertex (16): Tesseract

## External links[edit | edit source]

- Klitzing, Richard. "tibbit".