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    Discrete Math : Proof that there must be 12 Pentagons on a Soccer Ball

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    A soccer ball is formed by stitching together pieces of material that are regular pentagons and regular hexagons. Each corner of a polygon is the meeting place for exactly three polygons. Prove that there must be exactly 12 pentagons.
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    Solution Summary

    Euler's theorem is used to prove that there must be 12 Pentagons on a Soccer Ball. The solution is detailed and well presented. The solution received a rating of "5" from the student who posted the question.