A solid has forty faces and, sixty edges. Find the number of vertices of the solid.

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Solution

We know that,
Euler's Formula is valid for any polyhedrons. i.e.
$F + V - E = 2$
Given, $F = 40$ and $V = a$ and $E = 60$
According to the formula:
$40 + a - 60 = 2$
$a - 20 = 2$
$a = 20 + 2$
$a = 22 =$ number of vertices

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