Euler's formula and platonic solids

Sep 2012
96
0
U.K.
Totally flummoxed by this problem:


(a) Prove that for a convex polyhedron with V vertices, E edges and F faces, the following inequalities are true: 2E > 3F and 2E > 3V.

(b) Deduce using Euler’s formula that 2V > F + 4,3V > E + 6,2F > V + 4 and 3F > E + 6.

(c) Give an example of a convex polyhedron for which all these inequalities are equalities: 2E = 3V = 3F,2V = F + 4,3V = E + 6,2F = V + 4,3F = E + 6

(Note: All > mean greater than or equal to)