- Hyperbolic soccerball
The hyperbolic soccerball is a tiling of a surface frequently used as a manipulative for studying the properties of
hyperbolic geometry . It is an embedding of theorder-7 truncated triangular tiling into Euclidean space.Description
Just as hexagons surrounding pentagons can approximate a sphere on a
soccer ball, hexagons surrounding seven-sided heptagons can approximate a hyperbolic surface. The key feature of this model is that each vertex joins two hexagons with one heptagon, for a total of about 368.6°. This less than 10° excess over the 360° expected at each vertex on a flat surface causes the characteristic "negative curvature" of the hyperbolic surface. In contrast, a flat surface has "zero curvature" and a sphere has "positive curvature".History
This tiling was invented in January 2000 by Keith D. Henderson. He was prompted to experiment with different tilings after viewing less-satisfactory triangular tiling models made by his father, mathematician David W. Henderson of Cornell University. When he realized that the new tiling was similar to the tiling pattern on a soccer ball, the 'hyperbolic soccerball' moniker was born.
ee also
*
Truncated icosahedron External links
* [http://www.theiff.org/images/IFF_HypSoccerBall.pdf PDF with instructions]
* [http://www.liis.lv/datnod/izstade/slides/IMG_5278_par.html A rather large hyperbolic soccerball]
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