Order-7 square tiling

Order-7 square tiling
Poincaré disk model of the hyperbolic plane
Type	Hyperbolic regular tiling
Vertex figure	47
Schläfli symbol	{4,7}
Wythoff symbol	7 | 4 2
Coxeter diagram
Symmetry group	[7,4], (*742)
Dual	Order-4 heptagonal tiling
Properties	Vertex-transitive, edge-transitive, face-transitive

In geometry, the order-7 square tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {4,7}.

Related polyhedra and tiling

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

*n42 symmetry mutation of regular tilings: {4,n}
Spherical	Euclidean	Compact hyperbolic				Paracompact
{4,3}	{4,4}	{4,5}	{4,6}	{4,7}	{4,8}...	{4,∞}

Uniform heptagonal/square tilings
Symmetry: [7,4], (*742)							[7,4]+, (742)	[7+,4], (7*2)	[7,4,1+], (*772)
								60px
{7,4}	t{7,4}	r{7,4}	2t{7,4}=t{4,7}	2r{7,4}={4,7}	rr{7,4}	tr{7,4}	sr{7,4}	s{7,4}	h{4,7}
Uniform duals
V74	V4.14.14	V4.7.4.7	V7.8.8	V47	V4.4.7.4	V4.8.14	V3.3.4.3.7	V3.3.7.3.7	V77

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)

See also

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

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