It has been conjectured that every configuration C of convex objects in 3-space with disjoint interiors can be taken apart by translation with two hands: that is, some proper subset of C can be translated to infinity without disturbing its complement. We show that the conjecture holds for five or fewer objects and give a counterexample with six objects. We extend the counterexample to a configuration that cannot be taken apart with two hands using arbitrary isometries (rigid motions).
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