Question

Question 17

Which of the following cannot be true for a polyhedron?
(a) V = 4, F = 4, E = 6
(a) V = 6, F = 8, E = 12
(a) V = 20, F = 12, E = 30
(a) V = 4, F = 6, E = 6

Answer 1

We know that, Euler's formula for any polyhedron is F + V - E = 2
where, F = faces, V = vertices and E = edges
(a) V = 4, F = 4 and E = 6
LHS = F + V - E
= 4 + 4 - 6
= 8 - 6 = 2
= RHS

(b) V = 6, F = 8 and E = 12
LHS = F + V - E
= 8 + 6 -12
= 14 - 12 = 2
= RHS

(c) V = 20, F = 12 and E = 30
LHS = F + V - E
=12 + 20 - 30
= 32 - 30 = 2
= RHS

(d) V = 4, F = 6 and E = 6
LHS = F + V - E
= 6 + 4 - 6
= 10 - 6 = 4 $\ne$ RHS

$\therefore$ Option (d) is not true for a polyhedron.