HYPERBOLIC SOCCERBALL

The 'hyperbolic soccerball' is a tiling of a surface frequently used as a manipulative for studying the properties of hyperbolic geometry.

Contents

Description

History

See also

External links

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.

See also

★ Truncated icosahedron

External links

★ PDF with instructions

★ A rather large hyperbolic soccerball

★ An equivalent Poincaré model