Infinite-order pentagonal tiling

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Infinite-order pentagonal tiling
Infinite-order pentagonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic regular tiling
Vertex configuration 5
Schläfli symbol {5,∞}
Wythoff symbol ∞ | 5 2
Coxeter diagram CDel node.pngCDel infin.pngCDel node.pngCDel 5.pngCDel node 1.png
CDel node 1.pngCDel split1-55.pngCDel branch.pngCDel labelinfin.png
Symmetry group [∞,5], (*∞52)
Dual Order-5 apeirogonal tiling
Properties Vertex-transitive, edge-transitive, face-transitive

In 2-dimensional hyperbolic geometry, the infinite-order pentagonal tiling is a regular tiling. It has Schläfli symbol of {5,∞}. All vertices are ideal, located at "infinity", seen on the boundary of the Poincaré hyperbolic disk projection.

Symmetry[edit]

There is a half symmetry form, CDel node 1.pngCDel split1-55.pngCDel branch.pngCDel labelinfin.png, seen with alternating colors:

H2 tiling 55i-4.png

Related polyhedra and tiling[edit]

This tiling is topologically related as a part of sequence of regular polyhedra and tilings with vertex figure (5n).

Finite Compact hyperbolic Paracompact
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
Uniform tiling 58-t0.png
{5,8}...
CDel node 1.pngCDel 5.pngCDel node.pngCDel 8.pngCDel node.png
H2 tiling 25i-4.png
{5,∞}
CDel node 1.pngCDel 5.pngCDel node.pngCDel infin.pngCDel node.png

See also[edit]

References[edit]

  • John H. Conway; Heidi Burgiel; Chaim Goodman-Strass (2008). "Chapter 19, The Hyperbolic Archimedean Tessellations". The Symmetries of Things. ISBN 978-1-56881-220-5.
  • H. S. M. Coxeter (1999). "Chapter 10: Regular honeycombs in hyperbolic space". The Beauty of Geometry: Twelve Essays. Dover Publications. ISBN 0-486-40919-8. LCCN 99035678.

External links[edit]