# Hexadecachoric tetracomb

Hexadecachoric tetracomb | |
---|---|

Rank | 5 |

Type | Regular |

Space | Euclidean |

Notation | |

Bowers style acronym | Hext |

Coxeter diagram | o3o4o3o3x () |

Schläfli symbol | {3,3,4,3} |

Elements | |

Tera | 3N hexadecachora |

Cells | 24N tetrahedra |

Faces | 32N triangles |

Edges | 12N |

Vertices | N |

Vertex figure | Icositetrachoron, edge length 1 |

Measures (edge length 1) | |

Vertex density | |

Related polytopes | |

Army | Hext |

Regiment | Hext |

Dual | Icositetrachoric tetracomb |

Conjugate | None |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | U_{5} |

Convex | Yes |

Nature | Tame |

The **hexadecachoric tetracomb** or **hext**, also called the **demitesseractic tetracomb**, **16-cell tetracomb**, also **-honeycomb**, is one of three regular tetracombs or tessellations of 4D Euclidean space. 3 hexadecachora join at each face, and 24 join at each vertex of this honeycomb. It is the 4D demihypercubic honeycomb, obtained by alternation of the tesseractic tetracomb. It can also be formed as the hull of two dual tesseractic tetracombs, with the hexadecachoric facets being seen as square duotegums.

## Vertex coordinates[edit | edit source]

The vertices of a hexadecachoric tetracomb of edge length 1 are given by:

- ,

where i, j, k, and l are integers, and i+j+k+l is even.

These coordinates are due to the hexadecachoric tetracomb's construction as an alternated tesseractic tetracomb. Another set of coordinates, formed from two dual tesseractic tetracombs, are given by:

- ,
- .

where i, j, k, and l are integers.

## Representations[edit | edit source]

A hexadecachoric tetracomb has the following Coxeter diagrams:

- o3o4o3o3x () (full symmetry)
- x3o3o4o *b3o () (S
_{5}symmetry, demitesseractic tetracomb, facets of two types) - x3o3o *b3o *b3o () (Q
_{5}symmetry, facets of three types)

## External links[edit | edit source]

- Klitzing, Richard. "hext".
- Wikipedia contributors. "16-cell honeycomb".