Soccer balls are usually covered with a design based on regular pentagons and hexagons.

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

(In reply to My thoughts by Bryan)

We can note that a standard soccer ball is (equivalently) analogous to a regular icosahedron or a regular dodecahedron (both Platonic Solids).

The former has 20 (triangular) sides, and the latter has 12 (pentagonal) sides.

In the former case, we "place" a pentagon centered on each of 12 vertices and a hexagon centered on each of 20 faces. (This means 12 pentagons and 20 hexagons.)

In the latter case, we "place" a hexagon centered on each of 20 vertices and a pentagon centered on each of 12 faces. (Again, this means 12 pentagons and 20 hexagons.)
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Bryan is correct... there is no reason that it MUST be modeled in this way.

Posted by Thalamus on 2004-04-08 15:30:20