Objects that cannot be taken apart with two hands

摘要

It has been conjectured that every configuration C of convex objects in 3-space with disjoint interiorscan be taken apart by translation with two hands: that is, some propersubset of C can be translated to infinity withoutdisturbing its complement. We show that the conjecture holds for five orfewer objects and give a counterexample with six objects. We extend thecounterexample to a configuration that cannot be taken apart with twohands using arbitrary isometries (rigid motions).