Order-5 square tiling

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

Order-5 square tiling

Poincaré disk model of the hyperbolic plane
TypeHyperbolic regular tiling
Vertex configuration45
Schläfli symbol{4,5}
Wythoff symbol5 | 4 2
Coxeter diagram
Symmetry group[5,4], (*542)
DualOrder-4 pentagonal tiling
PropertiesVertex-transitive, edge-transitive, face-transitive
Spherical Hyperbolic tilings








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

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


  • John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, 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.

See also

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