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Dec 20, 2010 at 15:14 comment added Igor Rivin The same argument shows that there are finitely many orbits in the general case, btw. Classification of surfaces is a wonderful thing.
Dec 20, 2010 at 14:52 comment added Chris Schommer-Pries Thanks! This is the answer I was hoping for. Another great example of how MO is the fastest substance known to mathematics.
Dec 20, 2010 at 14:51 vote accept Chris Schommer-Pries
Dec 20, 2010 at 14:05 history answered Bruno Martelli CC BY-SA 2.5