Which of the following cannot be true for a polyhedron?

Option (a) V = 4, F = 4, E = 6

According to Euler’s formula, F + V-E = 2 where F = face, V = vertices and E = edge

So, from the given

⇒ 4 + 4-6 = 2

⇒ 8-6 = 2

⇒ 2 = 2

⇒LHS = RHS. it is true for a polyhedron

(b) V = 6, F = 8, E = 12

According to Euler’s formula, F + V-E = 2 where F = face, V = vertices and E = edge

So, from the given

⇒ 8 + 6-12 = 2

⇒ 14-12 = 2

⇒ 2 = 2

⇒LHS = RHS. it is true for a polyhedron

(c) V = 20, F = 12, E = 30

According to Euler’s formula, F + V-E = 2 where F = face, V = vertices and E = edge

So, from the given

⇒ 12 + 20-30 = 2

⇒ 32-30 = 2

⇒ 2 = 2

⇒LHS = RHS. it is true for a polyhedron

(d) V = 4, F = 6, E = 6

According to Euler’s formula, F + V-E = 2 where F = face, V = vertices and E = edge

So, from the given

⇒ 6 + 4-6 = 2

⇒ 10-6 = 4 = LHS

⇒ RHS = 2

⇒ LHS ≠ RHS. it is not true for a polyhedron