Spherical Tilings
Familiar to many millions, probably billions, of people world-wide
would be a tiling of the sphere with pentagons (black) and
hexagons (white) to form a soccer ball. In particular, 12 pentagons and
20 hexagons such that each pentagon is surrounded by five hexagons
and each hexagon is surrounded by three hexagons and three
pentagons in alternation. The design is symmetric enough to be 
pleasing and still fly or roll truly. The ball is asymmetric enough
to attract visual attention and flexible enough to absorb powerful 
kicks without permanent distortion. Players heading the ball are 
somewhat less likely to get a concussion than in days of old, for which everyone is thankful.
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