Order-5 square tiling

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
Order-5 square tiling
Order-5 square tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic regular tiling
Vertex configuration 45
Schläfli symbol {4,5}
Wythoff symbol 5 | 4 2
Coxeter diagram File:CDel node.pngFile:CDel 5.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node 1.png
Symmetry group [5,4], (*542)
Dual Order-4 pentagonal tiling
Properties Vertex-transitive, edge-transitive, face-transitive

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

[edit | edit source]
Spherical Hyperbolic tilings
File:Spherical pentagonal hosohedron.svg
{2,5}
File:CDel node 1.pngFile:CDel 2.pngFile:CDel node.pngFile:CDel 5.pngFile:CDel node.png 		File:Uniform tiling 532-t2.svg
{3,5}
File:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 5.pngFile:CDel node.png 		File:H2-5-4-primal.svg
{4,5}
File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 5.pngFile:CDel node.png 		File:H2 tiling 255-1.png
{5,5}
File:CDel node 1.pngFile:CDel 5.pngFile:CDel node.pngFile:CDel 5.pngFile:CDel node.png 		File:H2 tiling 256-1.png
{6,5}
File:CDel node 1.pngFile:CDel 6.pngFile:CDel node.pngFile:CDel 5.pngFile:CDel node.png 		File:H2 tiling 257-1.png
{7,5}
File:CDel node 1.pngFile:CDel 7.pngFile:CDel node.pngFile:CDel 5.pngFile:CDel node.png 		File:H2 tiling 258-1.png
{8,5}
File:CDel node 1.pngFile:CDel 8.pngFile:CDel node.pngFile:CDel 5.pngFile:CDel node.png 		... File:H2 tiling 25i-1.png
{∞,5}
File:CDel node 1.pngFile:CDel infin.pngFile:CDel node.pngFile:CDel 5.pngFile:CDel node.png

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
File:Uniform tiling 432-t0.png
{4,3}
File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.png 		File:Uniform tiling 44-t0.svg
{4,4}
File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node.png 		File:H2-5-4-primal.svg
{4,5}
File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 5.pngFile:CDel node.png 		File:H2 tiling 246-4.png
{4,6}
File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 6.pngFile:CDel node.png 		File:H2 tiling 247-4.png
{4,7}
File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 7.pngFile:CDel node.png 		File:H2 tiling 248-4.png
{4,8}...
File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 8.pngFile:CDel node.png 		File:H2 tiling 24i-4.png
{4,∞}
File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel infin.pngFile:CDel node.png
Uniform pentagonal/square tilings
Symmetry: [5,4], (*542) [5,4]+, (542) [5+,4], (5*2) [5,4,1+], (*552)
File:CDel node 1.pngFile:CDel 5.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node.png File:CDel node 1.pngFile:CDel 5.pngFile:CDel node 1.pngFile:CDel 4.pngFile:CDel node.png File:CDel node.pngFile:CDel 5.pngFile:CDel node 1.pngFile:CDel 4.pngFile:CDel node.png File:CDel node.pngFile:CDel 5.pngFile:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.png File:CDel node.pngFile:CDel 5.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node 1.png File:CDel node 1.pngFile:CDel 5.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node 1.png File:CDel node 1.pngFile:CDel 5.pngFile:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.png File:CDel node h.pngFile:CDel 5.pngFile:CDel node h.pngFile:CDel 4.pngFile:CDel node h.png File:CDel node h.pngFile:CDel 5.pngFile:CDel node h.pngFile:CDel 4.pngFile:CDel node.png File:CDel node.pngFile:CDel 5.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node h.png
File:H2-5-4-dual.svg File:H2-5-4-trunc-dual.svg File:H2-5-4-rectified.svg File:H2-5-4-trunc-primal.svg File:H2-5-4-primal.svg File:H2-5-4-cantellated.svg File:H2-5-4-omnitruncated.svg File:H2-5-4-snub.svg File:Uniform tiling 542-h01.png File:Uniform tiling 552-t0.png
{5,4} t{5,4} r{5,4} 2t{5,4}=t{4,5} 2r{5,4}={4,5} rr{5,4} tr{5,4} sr{5,4} s{5,4} h{4,5}
Uniform duals
File:CDel node f1.pngFile:CDel 5.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node.png File:CDel node f1.pngFile:CDel 5.pngFile:CDel node f1.pngFile:CDel 4.pngFile:CDel node.png File:CDel node.pngFile:CDel 5.pngFile:CDel node f1.pngFile:CDel 4.pngFile:CDel node.png File:CDel node.pngFile:CDel 5.pngFile:CDel node f1.pngFile:CDel 4.pngFile:CDel node f1.png File:CDel node.pngFile:CDel 5.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node f1.png File:CDel node f1.pngFile:CDel 5.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node f1.png File:CDel node f1.pngFile:CDel 5.pngFile:CDel node f1.pngFile:CDel 4.pngFile:CDel node f1.png File:CDel node fh.pngFile:CDel 5.pngFile:CDel node fh.pngFile:CDel 4.pngFile:CDel node fh.png File:CDel node fh.pngFile:CDel 5.pngFile:CDel node fh.pngFile:CDel 4.pngFile:CDel node.png File:CDel node.pngFile:CDel 5.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node fh.png
File:H2-5-4-primal.svg File:H2-5-4-kis-primal.svg File:H2-5-4-rhombic.svg File:H2-5-4-kis-dual.svg File:H2-5-4-dual.svg File:H2-5-4-deltoidal.svg File:H2-5-4-kisrhombille.svg File:H2-5-4-floret.svg File:Uniform tiling 552-t2.png
V54 V4.10.10 V4.5.4.5 V5.8.8 V45 V4.4.5.4 V4.8.10 V3.3.4.3.5 V3.3.5.3.5 V55

This hyperbolic tiling is related to a semiregular infinite skew polyhedron with the same vertex figure in Euclidean 3-space.

File:Five-square skew polyhedron.png

References

[edit | edit source]
  • John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value). (Chapter 19, The Hyperbolic Archimedean Tessellations)
  • Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).

See also

[edit | edit source]
Error creating thumbnail: File missing
Wikimedia Commons has media related to Order-5 square tiling.
[edit | edit source]


Stub icon

This hyperbolic geometry-related article is a stub. You can help Wikipedia by expanding it.

Retrieved from "http://70.231.62.181/index.php?title=Order-5_square_tiling&oldid=8378282"