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A flat ball? (Posted on 2004-04-08) Difficulty: 2 of 5
Soccer balls are usually covered with a design based on regular pentagons and hexagons.

How many pentagons/hexagons MUST there be, and why?

See The Solution Submitted by Federico Kereki    
Rating: 3.7500 (4 votes)

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re: A related question... | Comment 18 of 24 |
(In reply to A related question... by SilverKnight)

As it turns out, the number of hexagons must be 0 or 20.  If there was some other solid, then it would have been included as a 'Johnson Solid'.  Johnson solids are convex polyhedra which have all faces as regular polygons of unit length and are NOT Platonic solids, Archimedean solids, prisms or antiprisms.  The number of Johnson solids was proven to be 92, and none of those solids is composed of solely pentagons and hexagons.

See: http://mathworld.wolfram.com/JohnsonSolid.html

  Posted by Brian Smith on 2004-04-13 14:26:51

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