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If P pentagons and H hexagons are used, then there are F = P H faces, V = (5 P 6 H) / 3 vertices, and E = (5 P 6 H) / 2 edges The Euler characteristic is thus = = Because the sphere has Euler characteristic 2, it follows that P = 12 That is, a soccer ball constructed in this way always has 12 pentagons.
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