# Simplicial honeycomb

(n − 1)-simplex honeycomb | |
---|---|

Rank | n |

Type | Uniform |

Space | Euclidean |

Notation | |

Coxeter diagram | x3o3o3o...o3o3o3*a |

Elements | |

Cells | M tetrahedra, M octahedra |

Faces | M triangles |

Edges | M |

Vertices | M |

Vertex figure | Expanded n -simplex, edge length 1 |

Measures (edge length 1) | |

Vertex density | |

Related polytopes | |

Conjugate | None |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | P_{n } |

Convex | Yеs |

Nature | Tame |

The **simplicial honeycombs** form an infinite series of uniform tessellations. Their vertex figures are expanded simplexes.

## Examples[edit | edit source]

Rank | Name | Picture |
---|---|---|

2 | Apeirogon | |

3 | Triangular tiling | |

4 | Tetrahedral-octahedral honeycomb | |

5 | Cyclopentachoric tetracomb | |

6 | Cyclohexateric pentacomb | |

7 | Cycloheptapetic hexacomb | |

8 | Cyclooctaexic heptacomb |

## External links[edit | edit source]

- Wikipedia contributors. "Simplicial honeycomb".

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