User blog comment:Edwin Shade/The Origami Function/@comment-1605058-20171003171507

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Of other things, I would say that your definition of "well-defined" is not specific enough for your needs -- after all, you can have a fold along a line through a vertex forming a 30 degree angle with the edge, and this can be replicated precisely. I would suggest using something like Huzita-Hatori axioms which makes things mathematically precise.