Find the number of edges of the polyhedron having 7 faces and 10 vertices.

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Solution

The correct option is B 15
By the Euler's relation for polyhedron, we know that
Number of faces + Number of vertices = Number of edges + 2
or F + V = E + 2
Given: Number of faces = 7
Number of vertices = 10
Let the number of edges = x
Now substituting these values in the Euler's relation,
$F + V = E + 2$
$\Rightarrow 7 + 10 = x + 2$
$\Rightarrow x = 7 + 10 - 2$
$\Rightarrow x = 15.$

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