# Tesseractihexadecatruncated prismatotesseractihexadecachoron

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Tesseractihexadecatruncated prismatotesseractihexadecachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Thatpath |

Coxeter diagram | x3x3x4/3x4*b () |

Elements | |

Cells | 24 octagrammic prisms, 16 truncated octahedra, 8 great rhombicuboctahedra, 8 cuboctatruncated cuboctahedra |

Faces | 96+96 squares, 64+64 hexagons, 48 octagons, 48 octagrams |

Edges | 192+192+192+192 |

Vertices | 384 |

Vertex figure | Irregular tetrahedron, edge lengths √2 (2), √3 (2), √2+√2 (1), and √2–√2 (1) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Cotco–8/3–stop: 135° |

Toe–4–stop: 135° | |

Cotco–6–toe: 120° | |

Cotco–8–girco: 90° | |

Girco–4–stop: 90° | |

Toe–6–girco: 60° | |

Number of external pieces | 176 |

Level of complexity | 60 |

Related polytopes | |

Army | Semi-uniform Gidpith, edge lengths (octagons), 1 (bases of hexagonal prisms) |

Regiment | Thatpath |

Conjugate | Tesseractihexadecaquasitruncated prismatotesseractihexadecachoron |

Convex core | Tesseract |

Abstract & topological properties | |

Flag count | 9216 |

Euler characteristic | –24 |

Orientable | Yes |

Properties | |

Symmetry | B_{4}, order 384 |

Convex | No |

Nature | Tame |

The **tesseractihexadecatruncated prismatotesseractihexadecachoron**, or **thatpath**, is a nonconvex uniform polychoron that consists of 24 octagrammic prisms, 16 truncated octahedra, 8 great rhombicuboctahedra, and 8 cuboctatruncated cuboctahedra. 1 of each type of cell join at each vertex.

The tesseractihexadecatruncated prismatotesseractihexadecachoron can be vertex-inscribed into a disicositetratruncated disicositetrachoron.

## Cross-sections[edit | edit source]

## Vertex coordinates[edit | edit source]

Vertex coordinates for a tesseractihexadecatruncated prismatotesseractihexadecachoron of edge length 1 are given by all permutations of:

## External links[edit | edit source]

- Bowers, Jonathan. "Category 9: Omnitruncates" (#340).

- Klitzing, Richard. "thatpath".