standard polygon. The area formula follows from the Gauss–Bonnet theorem and is in a certain sense generalized through the Riemann–Hurwitz formula. Explicit form for standard polygons Explicit expressions can be given for the regular standard 4g-sided polygon, with rotational symmetry. In this case, that of a genus Riemann surface with g-fold rotational symmetry, the group may be given by generators . These generators are given by the following fractional linear transforms acting on the upper half-plane: for . The parameters are given by and and It may be verified that these generators obey the constraint which gives the totality of the group presentation. See also Cayley graph Euclidean domain Voronoi diagram Notes References Conformal geometry Riemann surfaces Combinatorial group theory Geometric topology