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Math Help - Euler's formula and platonic solids

  1. #1
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    Euler's formula and platonic solids

    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 Eulerís 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)
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  2. #2
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    Re: Euler's formula and platonic solids

    Hi,
    You need to know a little about polyhedra. If you don't understand statements in the attachment, you might skim the article Polyhedron - Wikipedia, the free encyclopedia.

    Euler's formula and platonic solids-mhfgeometry64.png
    Thanks from Deveno
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