Given a planar polygon (or chain) with a list of edges
we examine the effect of several operations that permute this edge list,
resulting in the formation of a new polygon. The main operations that
we consider are:
reversals which involve inverting the order of a sublist,
transpositions which involve interchanging subchains (sublists), and
edge-swaps which are a special case and involve
interchanging two consecutive edges.
Using these permuting operations,
we explore the complexity of performing certain actions,
such as convexifying a given polygon or obtaining its mirror image.
When each edge of the given polygon has also been assigned a direction
we say that the polygon is signed. In this case any edge involved in a
reversal changes direction. The complexity of some problems varies
depending on whether a polygon is signed or unsigned. An additional
restriction in many cases is that polygons remain simple after every