Order-4 pentagonal tiling

Order-4 pentagonal tiling
Order-4 pentagonal tiling
Order-4 pentagonal tiling
Poincaré disk model of the hyperbolic plane
Type Regular hyperbolic tiling
Vertex figure 5.5.5.5
Schläfli symbol(s) {5,4}
Wythoff symbol(s) 4 | 5 2
Coxeter-Dynkin(s) CDel node 1.pngCDel 5.pngCDel node.pngCDel 4.pngCDel node.png
Coxeter group [5,4]
Dual Order-5 square tiling
Properties Vertex-transitive, edge-transitive, face-transitive

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

Contents

Related polyhedra and tiling

This tiling is topologically related as a part of sequence of regular polyhedra and tilings with pentagonal faces, starting with the dodecahedron, with Schläfli symbol {5,n}, and Coxeter diagram CDel node 1.pngCDel 5.pngCDel node.pngCDel n.pngCDel node.png, progressing to infinity.

Uniform polyhedron-53-t0.png
{5,3}
CDel node 1.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node.png
Uniform tiling 54-t0.png
{5,4}
CDel node 1.pngCDel 5.pngCDel node.pngCDel 4.pngCDel node.png
Uniform tiling 55-t0.png
{5,5}
CDel node 1.pngCDel 5.pngCDel node.pngCDel 5.pngCDel node.png
Uniform tiling 56-t0.png
{5,6}
CDel node 1.pngCDel 5.pngCDel node.pngCDel 6.pngCDel node.png
Uniform tiling 57-t0.png
{5,7}
CDel node 1.pngCDel 5.pngCDel node.pngCDel 7.pngCDel node.png

This tiling is also topologically related as a part of sequence of regular polyhedra and tilings with four faces per vertex, starting with the octahedron, with Schläfli symbol {n,4}, and Coxeter diagram CDel node 1.pngCDel n.pngCDel node.pngCDel 4.pngCDel node.png, with n progressing to infinity.

Uniform polyhedron-34-t0.png
{3,4}
CDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
Uniform tiling 44-t0.png
{4,4}
CDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node.png
Uniform tiling 54-t0.png
{5,4}
CDel node 1.pngCDel 5.pngCDel node.pngCDel 4.pngCDel node.png
Uniform tiling 64-t0.png
{6,4}
CDel node 1.pngCDel 6.pngCDel node.pngCDel 4.pngCDel node.png
Uniform tiling 74-t0.png
{7,4}
CDel node 1.pngCDel 7.pngCDel node.pngCDel 4.pngCDel node.png
... Hyperbolic tiling o4o∞x.png
{∞,4}
CDel node 1.pngCDel infin.pngCDel node.pngCDel 4.pngCDel node.png

References

See also

External links