# Truncated order-7 square tiling

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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 t0,1{4,7}.

## Contents

*n42 symmetry mutation of truncated tilings: n.8.8
Symmetry
*n42
[n,4]
Spherical Euclidean Compact hyperbolicParacompact
*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 V5.8.8V6.8.8V7.8.8V8.8.8V.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
V74V4.14.14V4.7.4.7V7.8.8V47V4.4.7.4V4.8.14V3.3.4.3.7V3.3.7.3.7V77

## Related Research Articles

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 t0,2{4,5}.

In geometry, the truncated order-4 pentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t0,1{5,4}.

In geometry, the truncated order-5 square tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t0,1{4,5}.

In geometry, the truncated order-5 pentagonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of t0,1{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 t0,1{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 t1,2(4,3,3). It can also be named as a cantic octagonal tiling, h2{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 t0,1{6,5}.

In geometry, the pentahexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of r{6,5} or t1{6,5}.

In geometry, the truncated order-6 pentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t1,2{6,5}.

In geometry, the rhombipentahexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t0,2{6,5}.

## References

• 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.