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Tetrapentagonal tiling

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Tetrapentagonal tiling
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In geometry, the tetrapentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t1{4,5} or r{4,5}.

Tetrapentagonal tiling
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Poincaré disk model of the hyperbolic plane
TypeHyperbolic uniform tiling
Vertex configuration(4.5)2
Schläfli symbolr{5,4} or
rr{5,5} or
Wythoff symbol2 | 5 4
5 5 | 2
Coxeter diagram or
or
Symmetry group[5,4], (*542)
[5,5], (*552)
DualOrder-5-4 rhombille tiling
PropertiesVertex-transitive edge-transitive
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Symmetry

A half symmetry [1+,4,5] = [5,5] construction exists, which can be seen as two colors of pentagons. This coloring can be called a rhombipentapentagonal tiling.

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Dual tiling

The dual tiling is made of rhombic faces and has a face configuration V4.5.4.5:

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More information Symmetry: [5,4], (*542), [5,4]+, (542) ...
More information Symmetry: [5,5], (*552), [5,5]+, (552) ...
More information Symmetry*4n2 [n,4], Spherical ...
More information Symmetry*5n2 [n,5], Spherical ...

See also

References

  • 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.


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