# Blended triangular tiling

Blended triangular tiling | |
---|---|

File:Blended triangular tiling.png | |

Rank | 3 |

Type | Regular |

Space | Euclidean |

Notation | |

Schläfli symbol | {3,6}#{} |

Elements | |

Faces | ∞ skew hexagons |

Edges | ∞ |

Vertices | ∞ |

Vertex figure | Hexagon, 0 < edge length < 1 |

Related polytopes | |

Dual | Only exists abstractly |

Petrie dual | Petrial blended triangular tiling |

Topological properties | |

Orientable | Yes |

Properties | |

Convex | No |

The **blended triangular tiling** is a regular skew polyhedron that contains an infinite number of skew triangles, with 4 at each vertex. It can be obtained by blending the triangular tiling with a line segment (hence the name). It can be represented as the Schläfli symbol {3,6}#{}. The actual height of the blended triangular tiling can vary, however these are all considered to still be one polyhedron (just like how the skew square can vary in height but it is still considered the same regular polygon).

## Vertex coordinates[edit | edit source]

Vertex coordinates of a blended triangular tiling centered at the origin with edge length 1 and height h are given by

where i and j range over the integers, and H is (Note that must always be true for H to be a real number and for the blend to be non-degenerate).

## 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.