Question

If a convex polyhedron has 18 edges and 12 vertices, then how many faces does it have?

Answer 1

Use Euler's characteristic.

V - E + F = 2

Now substitute and solve for F.

   V - E + F = 2
12 - 18 + F = 2
        -6 + F = 2
               F = 8

Therefore the polyhedron has 8 faces.