We have seen that the use of polygons in modelling linkages is quite convenient, as the model in question can be used to determine whether a pair(or any number of pairs) of linkages are equivalent, and whether one can be moved into the other.  The effectiveness of this method can be enhanced through the use of a linear-time algorithm for reconfiguring linkages in the plane through a "flexing" of its hinges, but the analog in three dimensions remains both unbounded in its complexity and an area of study for Computational Geometers. 

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