Order-5 square tiling

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Order-5 square tiling
Order-5 square tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic regular tiling
Vertex figure 45
Schläfli symbol {4,5}
Wythoff symbol 5 | 4 2
Coxeter diagram CDel node.pngCDel 5.pngCDel node.pngCDel 4.pngCDel 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}.

Related polyhedra and tiling[edit]

Spherical Hyperbolic tilings
Spherical pentagonal hosohedron.png
{2,5}
CDel node 1.pngCDel 2.pngCDel node.pngCDel 5.pngCDel node.png
Uniform tiling 532-t2.png
{3,5}
CDel node 1.pngCDel 3.pngCDel node.pngCDel 5.pngCDel node.png
H2 tiling 245-1.png
{4,5}
CDel node 1.pngCDel 4.pngCDel node.pngCDel 5.pngCDel node.png
H2 tiling 255-1.png
{5,5}
CDel node 1.pngCDel 5.pngCDel node.pngCDel 5.pngCDel node.png
H2 tiling 256-1.png
{6,5}
CDel node 1.pngCDel 6.pngCDel node.pngCDel 5.pngCDel node.png
H2 tiling 257-1.png
{7,5}
CDel node 1.pngCDel 7.pngCDel node.pngCDel 5.pngCDel node.png
H2 tiling 258-1.png
{8,5}
CDel node 1.pngCDel 8.pngCDel node.pngCDel 5.pngCDel node.png
... H2 tiling 25i-1.png
{∞,5}
CDel node 1.pngCDel infin.pngCDel node.pngCDel 5.pngCDel node.png

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

Finite Euclidean Compact hyperbolic Paracompact
Uniform polyhedron-43-t0.png
{4,3}
CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.png
Uniform tiling 44-t0.png
{4,4}
CDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node.png
Uniform tiling 45-t0.png
{4,5}
CDel node 1.pngCDel 4.pngCDel node.pngCDel 5.pngCDel node.png
Uniform tiling 46-t0.png
{4,6}
CDel node 1.pngCDel 4.pngCDel node.pngCDel 6.pngCDel node.png
Uniform tiling 47-t0.png
{4,7}
CDel node 1.pngCDel 4.pngCDel node.pngCDel 7.pngCDel node.png
Uniform tiling 48-t0.png
{4,8}...
CDel node 1.pngCDel 4.pngCDel node.pngCDel 8.pngCDel node.png
H2 tiling 24i-4.png
{4,∞}
CDel node 1.pngCDel 4.pngCDel node.pngCDel infin.pngCDel node.png
Uniform pentagonal/square tilings
Symmetry: [5,4], (*542) [5,4]+, (542) [5+,4], (5*2) [5,4,1+], (*552)
CDel node 1.pngCDel 5.pngCDel node.pngCDel 4.pngCDel node.png CDel node 1.pngCDel 5.pngCDel node 1.pngCDel 4.pngCDel node.png CDel node.pngCDel 5.pngCDel node 1.pngCDel 4.pngCDel node.png CDel node.pngCDel 5.pngCDel node 1.pngCDel 4.pngCDel node 1.png CDel node.pngCDel 5.pngCDel node.pngCDel 4.pngCDel node 1.png CDel node 1.pngCDel 5.pngCDel node.pngCDel 4.pngCDel node 1.png CDel node 1.pngCDel 5.pngCDel node 1.pngCDel 4.pngCDel node 1.png CDel node h.pngCDel 5.pngCDel node h.pngCDel 4.pngCDel node h.png CDel node h.pngCDel 5.pngCDel node h.pngCDel 4.pngCDel node.png CDel node.pngCDel 5.pngCDel node.pngCDel 4.pngCDel node h.png
Uniform tiling 54-t0.png Uniform tiling 54-t01.png Uniform tiling 54-t1.png Uniform tiling 54-t12.png Uniform tiling 54-t2.png Uniform tiling 54-t02.png Uniform tiling 54-t012.png Uniform tiling 54-snub.png Uniform tiling 542-h01.png 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
CDel node f1.pngCDel 5.pngCDel node.pngCDel 4.pngCDel node.png CDel node f1.pngCDel 5.pngCDel node f1.pngCDel 4.pngCDel node.png CDel node.pngCDel 5.pngCDel node f1.pngCDel 4.pngCDel node.png CDel node.pngCDel 5.pngCDel node f1.pngCDel 4.pngCDel node f1.png CDel node.pngCDel 5.pngCDel node.pngCDel 4.pngCDel node f1.png CDel node f1.pngCDel 5.pngCDel node.pngCDel 4.pngCDel node f1.png CDel node f1.pngCDel 5.pngCDel node f1.pngCDel 4.pngCDel node f1.png CDel node fh.pngCDel 5.pngCDel node fh.pngCDel 4.pngCDel node fh.png CDel node fh.pngCDel 5.pngCDel node fh.pngCDel 4.pngCDel node.png CDel node.pngCDel 5.pngCDel node.pngCDel 4.pngCDel node fh.png
Uniform tiling 54-t2.png Order-5 tetrakis square tiling.png Order-5-4 quasiregular rhombic tiling.png Order-4 pentakis pentagonal tiling.png Uniform tiling 54-t0.png Deltoidal tetrapentagonal tiling.png Order-4 bisected pentagonal tiling.png Order-5-4 floret pentagonal tiling.png 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.

Five-square skew polyhedron.png

References[edit]

See also[edit]

External links[edit]