Order-7 square tiling

Order-7 square tiling
Poincaré disk model of the hyperbolic plane
Type	Hyperbolic regular tiling
Vertex configuration	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} v t e
Spherical	Euclidean	Compact hyperbolic				Paracompact
{4,3}	{4,4}	{4,5}	{4,6}	{4,7}	{4,8}...	{4,∞}

Uniform heptagonal/square tilings v t e
Symmetry: [7,4], (*742)							[7,4]+, (742)	[7+,4], (7*2)	[7,4,1+], (*772)
{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

This tiling is a part of regular series {n,7}:

Tiles of the form {n,7}
Spherical	Hyperbolic tilings v t e
{2,7}	{3,7}	{4,7}	{5,7}	{6,7}	{7,7}	{8,7}	...	{∞,7}

References

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

Wikimedia Commons has media related to Order-7 square tiling.