I believe the condition that "No two adjacent polygons have the same image under F" takes care of Andy's concern, and in fact that is the reason this condition was included. --Dan Andy wrote: << I wrote: << . . . * For any edge e of any one polygon, there are exactly two polygons that have e as a full edge. Two such polygons sharing exactly one full edge are called "adjacent". No two adjacent polygons have the same image under F.
If I were making the definition, I would add the condition here that the image under X of the two polygons adjacent to e includes an open neighborhood of every point in the image of e except possibly the vertices e connects. Or roughly speaking, the two faces adjacent to e are on "opposite sides" of the edge. Did you intend to include this condition? Are there polygons that satisfy your definition that do not satisfy this condition?
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