document.write( "Question 1004695: What is the relationship between the number of vertices, the number of faces and the number of edges of a triangular prism and a pyramid whose base is a regular triangle? \n" ); document.write( "
Algebra.Com's Answer #621092 by ikleyn(52797)\"\" \"About 
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\n" ); document.write( "What is the relationship between the number of vertices, the number of faces and the number of edges
\n" ); document.write( "of a triangular prism and a pyramid whose base is a regular triangle?
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\n" ); document.write( "\n" ); document.write( "For a triangular prism: F - E + V = 5 - 9 + 6 = 2,\r
\n" ); document.write( "\n" ); document.write( "    where F is the number of faces, E is the number of edges and V is the number of vertices.\r
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\n" ); document.write( "\n" ); document.write( "For a triangular pyramid: F - E + V = 4 - 6 + 4 = 2,\r
\n" ); document.write( "\n" ); document.write( "    the same number as for a triangular prism.\r
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\n" ); document.write( "\n" ); document.write( "It is the consequence of the famous  Euler's theorem.\r
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\n" ); document.write( "\n" ); document.write( "The fact that the base is a regular triangle,  is not essentially important.
\n" ); document.write( "The relation is valid for many polyhedra that are surfaces of convex solid bodies.  See the referred Wikipedia article. \r
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