One way (among many) to get a orientable surface of genus g is to take a regular hyperbolic (4g+2)-gon with interior angle = 2pi/(2g+1) and identify opposite sides. This gives a highly symmetrical hyperbolic surface whose universal cover is the hyperbolic plane. In a sense, "most" hyperbolic surfaces have no non-trivial orientation-preserving symmetries at all. --Dan On May 18, 2014, at 12:09 PM, Mike Stay <metaweta@gmail.com> wrote:

Klein's quartic can be formed by taking a quotient of the {7,3} tiling of the hyperbolic plane, with 24 heptagons in all. The result is a 3-holed torus.

Is there a general way to get n-holed toruses (n>2) from quotients of the hyperbolic plane? -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com

_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun