# Square tiling prism

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Square tiling prism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Euclidean |

Notation | |

Coxeter diagram | |

Elements | |

Cells | MN cubes, 2 square tilings |

Faces | 2MN+2MN squares |

Edges | MN+4MN |

Vertices | 2MN |

Vertex figure | Square pyramid |

Related polytopes | |

Army | * |

Regiment | * |

Dual | Square tiling tegum |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | R3×A1 |

Convex | Yes |

Nature | Tame |

The **square tiling prism** or **cubic slab honeycomb** is a prismatic uniform honeycomb of the Euclidean plane. It consists of 2 square tilings and ∞ cubes. Each vertex joins 1 square tiling and 4 cubes. It is a prism based on the square tiling.

It appears as a segment of the cubic honeycomb.

## Vertex coordinates[edit | edit source]

A square tiling prism of edge length 1 has vertex coordinates given by, where range over the integers:

## Semi-uniform variant[edit | edit source]

The apeirogonal prism has a semi-uniform variant of the form x y4o4o that maintains its full symmetry. This variant uses square prisms as its sides.

## External links[edit | edit source]

- Wikipedia contributors. "Convex uniform honeycomb#Frieze forms".