Order-7 square tiling
Order-7 square tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic regular tiling
Vertex configuration 47
Schläfli symbol {4,7}
Wythoff symbol 7 | 4 2
Coxeter diagram
Symmetry group [7,4], (*742)
Dual Order-4 heptagonal tiling
Properties Vertex-transitive, edge-transitive, face-transitive

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

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This tiling is topologically related as a part of sequence of regular polyhedra and tilings with vertex figure (4n).

*n42 symmetry mutation of regular tilings: {4,n}
Spherical Euclidean Compact hyperbolic Paracompact
 
{4,3}
     
 
{4,4}
     
 
{4,5}
     
 
{4,6}
     
 
{4,7}
     
 
{4,8}...
     
 
{4,∞}
     
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
                                                           
               
V74 V4.14.14 V4.7.4.7 V7.8.8 V47 V4.4.7.4 V4.8.14 V3.3.4.3.7 V3.3.7.3.7 V77

This tiling is a part of regular series {n,7}:

Tiles of the form {n,7}
Spherical Hyperbolic tilings
 
{2,7}
     
 
{3,7}
     
 
{4,7}
     
 
{5,7}
     
 
{6,7}
     
 
{7,7}
     
 
{8,7}
     
...  
{∞,7}
     

References

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  • John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, 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.

See also

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