SOLUTION: A cube has 8 vertices, 12 edges, and 6 square faces. A soccer ball has 12 pentagonal faces and 20 hexagonal faces. How many vertices and how many edges does a soccer ball have?

Question 1073777: A cube has 8 vertices, 12 edges, and 6 square faces. A soccer ball has 12 pentagonal faces and 20 hexagonal faces. How many vertices and how many edges does a soccer ball have?
Answer by ikleyn(52814) (Show Source): You can put this solution on YOUR website!
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A cube has 8 vertices, 12 edges, and 6 square faces. A soccer ball has 12 pentagonal faces and 20 hexagonal faces.
How many vertices and how many edges does a soccer ball have?
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The number of edges of the soccer ball is  E =  = 90.


Why I divided by 2 ?  - Because in this way I counted every edge TWICE.


To find the number of vertices of the soccer ball, use the Euler equality

F - E + V = (same as for a cube = 6 -12 + 8 = 2) = 2.

You just have for the soccer ball F = 12 + 20 = 22  and  E = 90.

Hence, V = 2 - F + E = 2 - 22 + 90 = 70.


Answer.  The soccer ball has 70 vertices.

On the Euler formula I mentioned in my post see this Wikipedia article
https://en.wikipedia.org/wiki/Euler_characteristic

https://en.wikipedia.org/wiki/Euler_characteristic

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