# Tesseractihexadecachoric prism

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Tesseractihexadecachoric prism | |
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File:Tesseractihexadecachoric prism.png | |

Rank | 5 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Tahp |

Coxeter diagram | x o4x3x3o () |

Elements | |

Tera | 16 truncated tetrahedral prisms, 8 truncated octahedral prisms, 2 tesseractihexadecachora |

Cells | 32 triangular prisms, 24 cubes, 64 hexagonal prisms, 32 truncated tetrahedra, 16 truncated octahedra |

Faces | 64 triangles, 48+96+96 squares, 128 hexagons |

Edges | 96+192+192 |

Vertices | 192 |

Vertex figure | Digonal disphenoidal pyramid, edge lengths 1, √2, √3 (base), √2 (legs) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Tope–hip–tuttip: 120° |

Tuttip–trip–tuttip: 120° | |

Tope–cube–tope: 90° | |

Tah–toe–tope: 90° | |

Tah–tut–tuttip: 90° | |

Height | 1 |

Central density | 1 |

Number of external pieces | 26 |

Level of complexity | 30 |

Related polytopes | |

Army | Tahp |

Regiment | Tahp |

Dual | Disphenoidal enneacontahexachoric tegum |

Conjugate | None |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{4}×A_{1}, order 768 |

Convex | Yes |

Nature | Tame |

The **tesseractihexadecachoric prism** or **tahp** is a prismatic uniform polyteron that consists of 2 tesseractihexadecachora, 8 truncated octahedral prisms, and 16 truncated tetrahedral prisms. 1 tesseractihexadecachoron, 2 truncated octahedral prisms, and 2 truncated tetrahedral prisms join at each vertex. As the name suggests, it is a prism based on the tesseractihexadecachoron, which also makes it a convex segmentoteron.

## Vertex coordinates[edit | edit source]

The vertices of a tesseractihexadecachoric prism of edge length 1 are given by all permutations and sign changes of the first four coordinates of:

- .

## External links[edit | edit source]

- Klitzing, Richard. "Tahp".