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gus_massalast Sunday at 3:50 PM1 replyview on HN

Tip: Count the edges. Imagine each edge has two sides/ribons. One side/ribon is white and the other is black.


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C-x_C-ftoday at 5:16 AM

You can even find the exact number of pentagons (or hexagons, or edges, or vertices) using the equation

V - E + F = 2

where V, E, F are the number of vertices, edges, and faces, respectively.

This holds for any polyhedron (and other shapes have similar equations possibly with a different right hand side) and the left hand side is called the Euler characteristic of the soccer ball (or any polyhedron).

Spoiler warning: the Wikipedia article for the Euler characteristic [0] has a worked out example specifically for the soccer ball.

[0] https://en.wikipedia.org/wiki/Euler_characteristic

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