# Tesseractic tetracomb

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Tesseractic tetracomb | |
---|---|

Rank | 5 |

Type | Regular |

Space | Euclidean |

Notation | |

Bowers style acronym | Test |

Coxeter diagram | x4o3o3o4o () |

Schläfli symbol | {4,3,3,4} |

Elements | |

Tera | N tesseracts |

Cells | 4N cubes |

Faces | 6N squares |

Edges | 4N |

Vertices | N |

Vertex figure | Hexadecachoron, edge length √2 |

Related polytopes | |

Army | Test |

Regiment | Test |

Dual | Tesseractic tetracomb |

Conjugate | None |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | R_{5} |

Convex | Yes |

The **tesseractic tetracomb** or **test**, also called the **tesseractic honeycomb**, is one of three regular tetracombs or tessellations of 4D Euclidean space. 4 tesseracts join at each face, and 16 join at each vertex of this honeycomb. It is the 4D hypercubic honeycomb.

## Vertex coordinates[edit | edit source]

The vertices of a tesseractic tetracomb of edge length 1 are given by (i, j, k, l), where i, j, k, and l are integers.

## Representations[edit | edit source]

A tesseractic tetracomb has the following Coxeter diagrams:

- x4o3o3o4o (full symmetry)
- x4o3o3o4x (as expanded tesseractic tetracomb)
- o3o3o *b3o4x (S5 symmetry, tesseracts of two types)

## Related polytopes[edit | edit source]

Name | OBSA | CD diagram | Picture |
---|---|---|---|

Tesseractic tetracomb | test | ||

Rectified tesseractic tetracomb | rittit | ||

Icositetrachoric tetracomb | icot | ||

Truncated tesseractic tetracomb | tattit | ||

Bitruncated tesseractic tetracomb | batitit | ||

Small rhombated tesseractic tetracomb | srittit | ||

Rectified icositetrachoric tetracomb | ricot | ||

Great rhombated tesseractic tetracomb | grittit | ||

Truncated icositetrachoric tetracomb | ticot | ||

Small prismated tesseractic tetracomb | sidpitit | ||

Prismatotruncated tesseractic tetracomb | potatit | ||

Prismatorhombated tesseractic tetracomb | prittit | ||

Great prismated tesseractic tetracomb | gippittit | ||

Tesseractic tetracomb | test | ||

Celliprismated tesseractic tetracomb | capotat | ||

Cellirhombated tesseractic tetracomb | scartit | ||

Celligreatorhombated tesseractic tetracomb | gicartit | ||

Celliprismatotruncated tesseractic tetracomb | captatit | ||

Great cellated tesseractic tetracomb | otatit |

## External links[edit | edit source]

- Klitzing, Richard. "test".

- Wikipedia Contributors. "Tesseractic honeycomb".