# Blended square tiling

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Blended square tiling | |
---|---|

Rank | 3 |

Type | Regular |

Space | Euclidean |

Notation | |

Schläfli symbol | ^{[1]} |

Elements | |

Faces | N skew squares |

Edges | 2N |

Vertices | 2N |

Vertex figure | Square, 0 < edge length < |

Related polytopes | |

Dual | Only exists abstractly |

Petrie dual | Petrial blended square tiling |

Abstract properties | |

Schläfli type | {4,4} |

Topological properties | |

Orientable | Yes |

Genus | 0 |

Properties | |

Convex | No |

The **blended square tiling** is a regular skew polyhedron that has an infinite amount of skew squares as faces joined together 4 at a vertex. It can be obtained by blending the square tiling with a line segment (hence the name). It can be represented as the Schläfli symbol {4,4}#{}. The actual height of the blended square tiling can vary, but it is considered to still be one polyhedron, just like how the skew square can vary in height but it is still considered the same polygon.

## Vertex coordinates[edit | edit source]

Vertex coordinates of a blended square 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]

## Bibliography[edit | edit source]

- jan Misali (2020). "there are 48 regular polyhedra"
- McMullen, Peter; Schulte, Egon (1997). "Regular Polytopes in Ordinary Space" (PDF).
*Discrete Computational Geometry*(47): 449–478. doi:10.1007/PL00009304.