Truncated order-7 square tiling | |
---|---|

Poincaré disk model of the hyperbolic plane | |

Type | Hyperbolic uniform tiling |

Vertex configuration | 8.8.7 |

Schläfli symbol | t{4,7} |

Wythoff symbol | 4 |

Coxeter diagram | |

Symmetry group | [7,4], (*742) |

Dual | Order-4 heptakis heptagonal tiling |

Properties | Vertex-transitive |

In geometry, the **truncated order-7 square tiling** is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t_{0,1}{4,7}.

*n42 symmetry mutation of truncated tilings: n.8.8 | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Symmetry * n42 [n,4] | Spherical | Euclidean | Compact hyperbolic | Paracompact | |||||||

*242 [2,4] | *342 [3,4] | *442 [4,4] | *542 [5,4] | *642 [6,4] | *742 [7,4] | *842 [8,4]... | *∞42 [∞,4] | ||||

Truncated figures | |||||||||||

Config. | 2.8.8 | 3.8.8 | 4.8.8 | 5.8.8 | 6.8.8 | 7.8.8 | 8.8.8 | ∞.8.8 | |||

n-kis figures | |||||||||||

Config. | V2.8.8 | V3.8.8 | V4.8.8 | V5.8.8 | V6.8.8 | V7.8.8 | V8.8.8 | V∞.8.8 |

Uniform heptagonal/square tilings | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Symmetry: [7,4], (*742) | [7,4]^{+}, (742) | [7^{+},4], (7*2) | [7,4,1^{+}], (*772) | ||||||||

{7,4} | t{7,4} | r{7,4} | 2t{7,4}=t{4,7} | 2r{7,4}={4,7} | rr{7,4} | tr{7,4} | sr{7,4} | s{7,4} | h{4,7} | ||

Uniform duals | |||||||||||

V7^{4} | V4.14.14 | V4.7.4.7 | V7.8.8 | V4^{7} | V4.4.7.4 | V4.8.14 | V3.3.4.3.7 | V3.3.7.3.7 | V7^{7} |

In geometry, the **triheptagonal tiling** is a semiregular tiling of the hyperbolic plane, representing a rectified Order-3 heptagonal tiling. There are two triangles and two heptagons alternating on each vertex. It has Schläfli symbol of r{7,3}.

In geometry, the **rhombitetrapentagonal tiling** is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t_{0,2}{4,5}.

In geometry, the **truncated order-4 pentagonal tiling** is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t_{0,1}{5,4}.

In geometry, the **truncated order-5 square tiling** is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t_{0,1}{4,5}.

In geometry, the **truncated order-5 pentagonal tiling** is a regular tiling of the hyperbolic plane. It has Schläfli symbol of t_{0,1}{5,5}, constructed from one pentagons and two decagons around every vertex.

In geometry, the **truncated order-4 heptagonal tiling** is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t{7,4}.

In geometry, the **tetraheptagonal tiling** is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of r{4,7}.

In geometry, the **order-7 square tiling** is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {4,7}.

In geometry, the **rhombitetraheptagonal tiling** is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of rr{4,7}. It can be seen as constructed as a rectified tetraheptagonal tiling, r{7,4}, as well as an expanded order-4 heptagonal tiling or expanded order-7 square tiling.

In geometry, the **truncated tetraheptagonal tiling** is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of tr{4,7}.

In geometry, the **snub tetraheptagonal tiling** is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of sr{7,4}.

In geometry, the **order-7 heptagonal tiling** is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {7,7}, constructed from seven heptagons around every vertex. As such, it is self-dual.

In geometry, the **truncated order-7 heptagonal tiling** is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t_{0,1}{7,7}, constructed from one heptagons and two tetrakaidecagons around every vertex.

In geometry, the **snub heptaheptagonal tiling** is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of sr{7,7}, constructed from two regular heptagons and three equilateral triangles around every vertex.

In geometry, the **tritetratrigonal tiling** or **shieldotritetragonal tiling** is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t_{1,2}(4,3,3). It can also be named as a **cantic octagonal tiling**, h_{2}{8,3}.

In geometry, the **alternated order-4 hexagonal tiling** is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of (3,4,4), h{6,4}, and hr{6,6}.

In geometry, the **truncated order-5 hexagonal tiling** is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t_{0,1}{6,5}.

In geometry, the **pentahexagonal tiling** is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of r{6,5} or t_{1}{6,5}.

In geometry, the **truncated order-6 pentagonal tiling** is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t_{1,2}{6,5}.

In geometry, the **rhombipentahexagonal tiling** is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t_{0,2}{6,5}.

- John H. Conway, Heidi Burgiel, Chaim Goodman-Strass,
*The Symmetries of Things*2008, ISBN 978-1-56881-220-5 (Chapter 19, The Hyperbolic Archimedean Tessellations) - "Chapter 10: Regular honeycombs in hyperbolic space".
*The Beauty of Geometry: Twelve Essays*. Dover Publications. 1999. ISBN 0-486-40919-8. LCCN 99035678.

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