Quarter order-6 square tiling explained

bgcolor=#e7dcc3 colspan=2	Quarter order-6 square tiling
align=center colspan=2	Poincaré disk model of the hyperbolic plane
bgcolor=#e7dcc3 width=110	Type	Hyperbolic uniform tiling
Vertex figure	3.4.6.6.4
Schläfli symbol	q
Coxeter diagram	= = = or or or
Dual	?
Properties	Vertex-transitive

In geometry, the quarter order-6 square tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of q. It is constructed from *3232 orbifold notation, and can be seen as a half symmetry of *443 and *662, and quarter symmetry of *642.

Images

Projections centered on a vertex, triangle and hexagon:

See also

• Square tiling
• Tilings of regular polygons
• List of uniform planar tilings
• List of regular polytopes

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.

External links

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