ABSTRACT
First, some basic definitions are in order. A fold refers to any folded paper object, independent of the number of folds done in sequence. The crease pattern of a fold is a planar embedding of a graph which represents the creases that are used in the final folded object. (This can be thought of as a structural blueprint of the fold.) Creases come in two types: mountain creases, which are convex, and valley creases, which are concave (see Figure 1). Clearly the type of a crease depends on which side of the paper we look at, and so we assume we are always looking at the same side of the paper.
