Order-5 square tiling

Order-5 square tiling
Poincaré disk model of the hyperbolic plane
Type	Regular hyperbolic tiling
Vertex figure	45
Schläfli symbol(s)	{4,5}
Wythoff symbol(s)	5 | 4 2
Coxeter-Dynkin(s)
Coxeter group	[5,4]
Dual	Order-4 pentagonal tiling
Properties	Vertex-transitive, edge-transitive, face-transitive

In geometry, the order-5 square tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {4,5}.

Related polyhedra and tiling

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

{4,3}

{4,4}

{4,5}

{4,6}

{4,7}

{4,8}

...

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)
• Coxeter, The Beauty of Geometry: Twelve Essays (1999), Dover Publications, LCCN 99-35678, ISBN 0-486-40919-8 (Chapter 10: Regular honeycombs in hyperbolic space)

See also

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

External links

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

This geometry-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Tiling Geometry stubs Wikimedia Foundation. 2010. Игры ⚽ Нужен реферат? Mike Rama German submarine U-77 Look at other dictionaries: Order-4 pentagonal tiling — Poincaré disk model of the hyperbolic plane Type Regular hyperbolic tiling Vertex figure 5.5.5.5 Schläfli symbol(s) …   Wikipedia Order-7 triangular tiling — Poincaré disk model of the hyperbolic plane Type Regular hyperbolic tiling Vertex figure 37 Schläfli symbol(s) …   Wikipedia Snub square tiling — In geometry, the snub square tiling is a semiregular tiling of the Euclidean plane. There are three triangles and two squares on each vertex. It has Schläfli symbol of s{4,4} .Conway calls it a snub quadrille, constructed as a snub operation… …   Wikipedia Order-3 bisected heptagonal tiling — Type Dual semiregular hyperbolic tiling Faces Right triangle Face configuration V4.6.14 …   Wikipedia Squaring the square — is the problem of tiling an integral square using only other integral squares. (An integral square is a square whose sides have integer length.) The name was coined in a humorous analogy with squaring the circle. Squaring the square is an easy… …   Wikipedia Great rhombitriheptagonal tiling — In geometry, the great rhombitrihexagonal tiling (or omnitruncated trihexagonal tiling ) is a semiregular tiling of the Euclidean plane. There are one square, one hexagon, and one tetrakaidecagon(14 sides) on each vertex. It has Schläfli symbol… …   Wikipedia Elongated triangular tiling — In geometry, the elongated triangular tiling is a semiregular tiling of the Euclidean plane. There are three triangles and two squares on each vertex.Conway calls it a isosnub quadrille.There are 3 regular and 8 semiregular tilings in the… …   Wikipedia Aperiodic tiling — are an aperiodic set of tiles, since they admit only non periodic tilings of the plane:] Any of the infinitely many tilings by the Penrose tiles is non periodic. More informally, many refer to the Penrose tilings as being aperiodic tilings , but… …   Wikipedia Domino tiling — of a square A domino tiling of a region in the Euclidean plane is a tessellation of the region by dominos, shapes formed by the union of two unit squares meeting edge to edge. Equivalently, it is a matching in the grid graph formed by placing a… …   Wikipedia Bisected hexagonal tiling — Type Dual semiregular tiling Faces 30 60 90 triangle Face configuration V4.6.12 …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”