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Jan 24, 2010 at 19:22 comment added Joseph Malkevitch Since planar 3-connected graphs correspond to 3-polytopal graphs by Steinitz's Theorem one typically starts with an equation, say (), derived from Euler's polyhedral formula.This formula can involve only numbers of faces or it can involve numbers of faces and vertices. If one successfully constructs a polyhedron whose values satisfy the equation () one tries to find another solution that satisfies (*) by using graph theory ideas to make some "local change" in the graph that solved the original case. Perhaps if you are more specific about the problem that interests I can be more specific.
Jan 24, 2010 at 18:27 comment added Ali Dino Jumani I am writing the terms "Explicit set of Tools" or the " Mathematical Tools" ; which means the mathematical machinary needed to enumerate face vectors associated with polyhedron, to calculate the combinatorial types.
Jan 24, 2010 at 17:56 history answered David E Speyer CC BY-SA 2.5