Question 26

Fill in the blanks to make the statement true.

If a solid shape has 12 faces and 20 vertices, then the number of edges in this solid is ___.

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Solution

We know that, Euler's formula for any polyhedron is, F + V - E = 2
Given, faces (F) = 12, vertices (V) = 20
Now, on putting the value of F and V in the Euler's formula, we get 12 + 20 - E = 2
$\Rightarrow$ 32 - E = 2 $\Rightarrow$ 32 - 2 = E $\Rightarrow$ E = 30
Hence, the number of edges = 30

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