11 Nov
2011
11 Nov
'11
3:41 p.m.
Warren, I don't seem to have received the original message, at least not recently. Can you please state what is is you are responding to? Thanks, Dan << just use Euler characteristic x=V-E+F for polyhedra with V vertices E edges F faces. For genus g x=2-2g=#handles. For polyhedra of type "sphere" x=2. (example cube: V=8, E=12, F=6). For polyhedra of type "torus" x=0. For polyhedra of type "K spheres" we have x=2K. For polyhedra of type "sets of surfaces" the Euler characteristics obviously sum. So this whole problem becomes totally trivial if you view in terms of Euler. The end.
Even though kleptomaniacs can't help themselves, they do.