Abstract
It has been conjectured that every configurationC of convex objects in 3-space with disjoint interiors can be taken apart by translation with two hands: that is, some proper subset ofC 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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The research of J. Snoeyink was supported in part by an NSERC Research Grant. J. Stolfi was previously at DEC Systems Research Center, Palo Alto, CA, USA.
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Snoeyink, J., Stolfi, J. Objects that cannot be taken apart with two hands. Discrete Comput Geom 12, 367–384 (1994). https://doi.org/10.1007/BF02574386
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DOI: https://doi.org/10.1007/BF02574386