- Source: Truncated order-7 triangular tiling
In geometry, the order-7 truncated triangular tiling, sometimes called the hyperbolic soccerball, is a semiregular tiling of the hyperbolic plane. There are two hexagons and one heptagon on each vertex, forming a pattern similar to a conventional soccer ball (truncated icosahedron) with heptagons in place of pentagons. It has Schläfli symbol of t{3,7}.
Hyperbolic soccerball (football)
This tiling is called a hyperbolic soccerball (football) for its similarity to the truncated icosahedron pattern used on soccer balls. Small portions of it as a hyperbolic surface can be constructed in 3-space.
Dual tiling
The dual tiling is called a heptakis heptagonal tiling, named for being constructible as a heptagonal tiling with every heptagon divided into seven triangles by the center point.
Related tilings
This hyperbolic tiling is topologically related as a part of sequence of uniform truncated polyhedra with vertex configurations (n.6.6), and [n,3] Coxeter group symmetry.
From a Wythoff construction there are eight hyperbolic uniform tilings that can be based from the regular heptagonal tiling.
Drawing the tiles colored as red on the original faces, yellow at the original vertices, and blue along the original edges, there are 8 forms.
In popular culture
This tiling features prominently in HyperRogue.
See also
Triangular tiling
Order-3 heptagonal tiling
Order-7 triangular tiling
Tilings of regular polygons
List of uniform tilings
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.
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
Geometric explorations on the hyperbolic football by Frank Sottile
Kata Kunci Pencarian:
- Daftar bentuk matematika
- Truncated order-7 triangular tiling
- Truncated order-8 triangular tiling
- Triangular tiling
- Truncated infinite-order triangular tiling
- Truncated trihexagonal tiling
- Hexagonal tiling
- Truncated hexagonal tiling
- Trihexagonal tiling
- Truncated heptagonal tiling
- Uniform tilings in hyperbolic plane
