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Permalink In reply to by Anonymous (not verified)

Think of a cube. This has 6 faces, 12 edges and 8 vertices, so E-V=4
Now take one of the edges, and add a midpoint vertex. This divides the edge into two, so you also end up adding an edge ( and two of the faces now have 5 edges instead of 4, but that is irrelevant) So now you have E=13,V=9 and still E-V=4

It is clear that this can be repeated as many times as you want. So yes, there are really an unlimited number of possibilities!

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