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?
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-> 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?
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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(52812) (Show Source):
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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.
