Order-7 square tiling
Appearance
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
[edit]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) | ||||||||
{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 | |||||||
{2,7} |
{3,7} |
{4,7} |
{5,7} |
{6,7} |
{7,7} |
{8,7} |
... | {∞,7} |
References
[edit]- 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
[edit]Wikimedia Commons has media related to Order-7 square tiling.
External links
[edit]- 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