# Triangular tiling prism

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Triangular tiling prism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Euclidean |

Notation | |

Coxeter diagram | o6o3x2x () |

Elements | |

Cells | ∞ triangular prisms, 2 triangular tilings |

Faces | ∞ triangles, ∞ squares |

Edges | ∞+∞ |

Vertices | ∞ |

Vertex figure | Hexagonal pyramid |

Related polytopes | |

Army | Triangular tiling prism |

Regiment | Triangular tiling prism |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | V_{3}×A_{1} |

Convex | Yes |

Nature | Tame |

The **triangular tiling prism** is a prismatic uniform honeycomb of the Euclidean plane. It consists of 2 triangular tilings and ∞ triangular prisms. Each vertex joins 1 square tiling and 6 triangular prisms. It is a prism based on the triangular tiling.

## Vertex coordinates[edit | edit source]

A triangular tiling prism of edge length 1 has vertex coordinates given by:

- ,

where i and j range over the integers.

Integral coordinates can be given in 4 dimensions:

- ,

where i and j range over the integers.

## Representations[edit | edit source]

A triangular tiling prism has the following Coxeter diagrams:

- x2o6o3x () (full symmetry)
- x2x3o3o3*b () (P
_{3}×A_{1}symmetry, triangles considered of two types) - x2s6o3o () (alternated hexagonal tiling prism)
- x2o6s3s ()
- x2s3s3s3*b ()

## External links[edit | edit source]

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