Abstract
is true for cubes, pyramids, prisms, octahedra, and many other polyhedra. One might be tempted to think (as Euler himself apparently did) that this equality holds for all polyhedra, but it is easily seen that it fails for the picture frame of FIGURE l(a). Here v = 16, e = 32 and f = 16 so v e + f = 0. The discrepancy is usually dealt with by saying that (1) holds only for polyhedra without any holes, and then rewriting it in the form
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