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By the Euler characteristic for polyhedra, F + V = E + 2

where F = # faces, E = # egdes, V = # vertices.

The equation implies that E - V = F - 2

Thus, if the polyhedron solid has more than two faces (it must have at least 4) then the right hand side is positive. So the left hand side must be positive. That is, E must be greater than V.

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