# Blended hexagonal tiling

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Blended hexagonal tiling | |
---|---|

File:Blended hexagonal tiling.png | |

Rank | 3 |

Type | Regular |

Space | Euclidean |

Notation | |

Schläfli symbol | {6,3}#{} |

Elements | |

Faces | Infinite skew hexagons |

Edges | Infinite |

Vertices | Infinite |

Vertex figure | Triangle, 0 < edge length < |

Topological properties | |

Orientable | Yes |

Properties | |

Convex | No |

The **blended hexagonal tiling** is a regular skew polyhedron consisting of an infinite amount of skew hexagons, with 3 at a vertex. It can be obtained as the blend of a line segment and a hexagonal tiling, and so it has a Schlafli symbol of {6,3}#{}. It is abstractly identical to the hexagonal tiling. Just like the skew hexagon, the blended hexagonal tiling can vary in height but it is considered one polyhedron.

## Vertex coordinates[edit | edit source]

The vertex coordinates of a blended hexagonal tiling centered at the origin with edge length 1 and height h are

where i and j range over the integers, and H = .

## References[edit | edit source]

- jan Misali (2020). "there are 48 regular polyhedra"
- McMullen, Peter; Schulte, Egon (1997). "Regular Polytopes in Ordinary Space". Discrete Computational Geometry. 17: 449–478.