Question
Check whether a polyhedron can have $V = 12, E = 6$ and $F = 8$.
✓
Answer
By using Euler's formula for polyhedron,$F + V - E = 2$
[where, $F =$ faces, $V =$ vertices, $E =$ edges]
$\Rightarrow 8 + 12 - 6 = 2$
$\Rightarrow 20 - 6 = 2$
$\Rightarrow14\neq2$
$\therefore$ Given values do not satisfy the Euler's formula. Its mean this type of polyhedron cannot be possible.
[where, $F =$ faces, $V =$ vertices, $E =$ edges]
$\Rightarrow 8 + 12 - 6 = 2$
$\Rightarrow 20 - 6 = 2$
$\Rightarrow14\neq2$
$\therefore$ Given values do not satisfy the Euler's formula. Its mean this type of polyhedron cannot be possible.
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