Question

Which of the following can not be the property of a polyhedron?

• A. F = 4, V = 4 and E = 6
• B. F = 12, V = 20 and E = 30
• C. F = 6, V = 4 and E = 6
• D. F = 8, V = 6 and E = 12

Answer 1

The correct option is C F = 6, V = 4 and E = 6

By the Euler's Relation, we know that
F + V = E + 2.

If F = 4, V = 4 and E = 6
$\Rightarrow 4+4=6+2$
$\Rightarrow 8=8$
Hence, F + V = E + 2. So, it is true for polyhedron.

If F = 12, V = 20 and E = 30
$\Rightarrow 12+20=30+2$
$\Rightarrow 32=32$
Hence, F + V = E + 2. So, it is true for polyhedron.

If F = 6, V = 4 and E = 6
$\Rightarrow 6+4=6+2$
$\Rightarrow 10\ne 8$
Hence, $F+V\ne E+2.$ So, it is not true for polyhedron.

If F = 8, V = 6 and E = 12
$\Rightarrow 8+6=12+2$
$\Rightarrow 14=14$
Hence, F + V = E + 2. So, it is true for polyhedron.