Andy writes: << I wrote:
Wait -- consider any 3 consecutive (ccw) vertices A,B,C of a convex n-gon. If the triangle ABC is cut from the n-gon and re-glued so that they now appear in ccw order C,B,A, then it's easy to see that doesn't change the circumcircle (by its symmetry about the perpendicular bisector of AC). Since all permutations of the cyclic ordeer of the edges are generated by ones of this sort,
Actually, they aren't, if the polygon has an even number of sides. Color the sides alternately red and blue, and note that your permutations always switch edges of the same color.
What I intended to convey above is the operation of cutting off from the polygon the triangle whose vertices are 3 consecutive vertices A,B,C of the polygon (and therefore containing two consecutive edges AB and BC of the polygon), and gluing ABC back with AC reversed. The net result is that two adjacent edges of the polyong hav e been switched. These operations must generate the group of all permutations of the polygon edges. --Dan