# Blended hexagonal tiling

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 . 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.

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

Rank | 3 |

Type | Regular |

Space | Euclidean |

Notation | |

Schläfli symbol | |

Elements | |

Faces | N skew hexagons |

Edges | 3N |

Vertices | 2N |

Vertex figure | Triangle, 0 < edge length < |

Abstract & topological properties | |

Orientable | Yes |

Genus | 0 |

Properties | |

Convex | No |

## Vertex coordinatesEdit

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 .

## ReferencesEdit

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