Abstract Algebra 67: The number of rotational symmetries of a soccer ball 

Abstract Algebra 67: The number of rotational symmetries of a soccer ball
Abstract: We use group actions and the orbit stabilizer theorem to count the number of rotational symmetries of the soccer ball, in two different ways! First, we do so by thinking of these rotations as acting on the 12 pentagons of the soccer ball. Next, we do so by thinking of these rotations as acting on the 20 hexagons of the soccer ball. We of course get the same answer via either form of counting!
This video accompanies the class "Introduction to Abstract Algebra" at Colorado State University:
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