http://gdea.informatik.uni-koeln.de/599/ The Three Dimensional Logic Engine Kitching, Matthew Whitesides, Sue Z.250 Geometry We consider the following graph embedding question: given a graph G, is it possible to map its vertices to points in 3D such that G is isomorphic to the mutual nearest neighbor graph of the set P of points to which the vertices are mapped? We show that this problem is NP-hard. We do this by extending the "logic engine" method to three dimensions by using building blocks inpired by the structure of diamond and by constructions of A.G. Bell and B. Fuller. Springer Pach, János 2004 Conference Paper NonPeerReviewed Kitching, Matthew and Whitesides, Sue (2004) The Three Dimensional Logic Engine. [Conference Paper] http://gdea.informatik.uni-koeln.de/599/