document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #688681 by ikleyn(52814) $\"\"$ $\"About$

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\n" ); document.write( "A cube has 8 vertices, 12 edges, and 6 square faces. A soccer ball has 12 pentagonal faces and 20 hexagonal faces.
\n" ); document.write( "How many vertices and how many edges does a soccer ball have?
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document.write( "The number of edges of the soccer ball is  E =  = 90.\r\n" );
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document.write( "Why I divided by 2 ?  - Because in this way I counted every edge TWICE.\r\n" );
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document.write( "To find the number of vertices of the soccer ball, use the Euler equality\r\n" );
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document.write( "F - E + V = (same as for a cube = 6 -12 + 8 = 2) = 2.\r\n" );
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document.write( "You just have for the soccer ball F = 12 + 20 = 22  and  E = 90.\r\n" );
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document.write( "Hence, V = 2 - F + E = 2 - 22 + 90 = 70.\r\n" );
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document.write( "Answer.  The soccer ball has 70 vertices.\r\n" );
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\n" ); document.write( "\n" ); document.write( "On the Euler formula I mentioned in my post see this Wikipedia article\r
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\n" ); document.write( "\n" ); document.write( "https://en.wikipedia.org/wiki/Euler_characteristic\r
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