Q. 84.6( 57 Votes )

Can a polyhedron have 10 faces, 20 edges and 15 vertices?

Answer :

Number of faces = F = 10

Number of edges = E = 20


Number of vertices = V = 15


Any polyhedron satisfies Euler's Formula, according to which, F + V - E = 2


For the given polygon,


F + V - E = 10 + 15 - 20


= 25 - 20


= 5 ≠ 2


Since Euler's formula is not satisfied, such a polyhedron is not possible


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