Quarter order-6 square tiling

In geometry, the quarter order-6 square tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of q{4,6}. It is constructed from *3232 orbifold notation, and can be seen as a half symmetry of *443 and *662, and quarter symmetry of *642.

Quarter order-6 square tiling
Poincaré disk model of the hyperbolic plane
Type	Hyperbolic uniform tiling
Vertex figure	3.4.6.6.4
Schläfli symbol	q{4,6}
Coxeter diagram	= = = or or or
Dual	?
Properties	Vertex-transitive

Images

Projections centered on a vertex, triangle and hexagon:

Related polyhedra and tiling

Similar H2 tilings in *3232 symmetry
Coxeter diagrams
Vertex figure	6^6		(3.4.3.4)^2		3.4.6.6.4		6.4.6.4
Image
Dual

Uniform (4,4,3) tilings
Symmetry: [(4,4,3)] (*443)							[(4,4,3)]^+ (443)	[(4,4,3^+)] (3*22)	[(4,1^+,4,3)] (*3232)
h{6,4} t0(4,4,3)	h2{6,4} t0,1(4,4,3)	{4,6}^1/2 t1(4,4,3)	h2{6,4} t1,2(4,4,3)	h{6,4} t2(4,4,3)	r{6,4}^1/2 t0,2(4,4,3)	t{4,6}^1/2 t0,1,2(4,4,3)	s{4,6}^1/2 s(4,4,3)	hr{4,6}^1/2 hr(4,3,4)	h{4,6}^1/2 h(4,3,4)	q{4,6} h1(4,3,4)
Uniform duals
V(3.4)^4	V3.8.4.8	V(4.4)^3	V3.8.4.8	V(3.4)^4	V4.6.4.6	V6.8.8	V3.3.3.4.3.4	V(4.4.3)^2	V6^6	V4.3.4.6.6

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-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.

External links

• Weisstein, Eric W. "Hyperbolic tiling". MathWorld.
• Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld.
• Hyperbolic and Spherical Tiling Gallery
• KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
• Hyperbolic Planar Tessellations, Don Hatch