Order-5 square tiling explained

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

Related polyhedra and tiling

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.

References

• John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, (Chapter 19, The Hyperbolic Archimedean Tessellations)
• Book: The Beauty of Geometry: Twelve Essays. 1999. Dover Publications. 99035678. 0-486-40919-8. Chapter 10: Regular honeycombs in hyperbolic space.

See also

• Square tiling
• Uniform tilings in hyperbolic plane
• List of regular polytopes
• Medial rhombic triacontahedron

External links

• • • Hyperbolic and Spherical Tiling Gallery
• KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
• Hyperbolic Planar Tessellations, Don Hatch