A soccer ball has 20 faces that are regular hexagons and 12 faces that are regular pentagons. Use Theorem 7.4 to explain why a soccer ball cannot have a 60° rotational symmetry about a line through the centers of two opposite hexagonal faces.
Reference:
Theorem 7.4 Orbit-Stabilizer Theorem
Let G be a finite group of permutations of a set S. Then, for any i from S, |G| = |orbG(i)| |stabG(i)|.
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