This polyhedron discussion has been severely hampered by the absence of a definition of polyhedron. (There are many different definitions.) E.g., imagine a square with edges drawn from the center to its 4 corners and also to its 4 side-midpoints. Now identify opposite sides of the square in the usual way to get a torus. You end up with 8 faces, 12 edges, and 4 vertices. --Dan WFL wrote: << On 8/9/09, James Propp <jpropp@cs.uml.edu> wrote:
Oops: make that 4 vertices, 12 edges, and 8 faces (check: 4-12+8=0).
I don't think this can be correct. The only polyhedron with 4 vertices is a tetrahedron (4-6+4 = 2). WFL
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