Question

Question 72

Check whether a polyhedron can have V = 12, E = 6 and F = 8.

Answer 1

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
$\Rightarrow$ 14 $\ne$ 2
$\therefore$ Given values do not satisfy the Euler's formula. Its mean this type of polyhedron cannot be possible.