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