In article <C8EGuw.L0C@liverpool.ac.uk> email@example.com (Dr. C.D. Wright) writes: >Joseph O'Rourke (firstname.lastname@example.org) wrote: > >: There is a nice new advance on this problem by Snoeyink >: and Stolfi: "Objects that cannot be taken apart by two hands," >: 9th ACM Symp. Comp. Geom., 1993, 247-256. They show that a >: collection of convex objects in 3D cannot always be partitioned into >: two sets such that each can be translated to infinity without hitting >: the other. > >Perhaps I wasn't clear enough, but that isn't a new result. >Bob Dawson constructed a collection of 12 convex objects that >can only be taken apart by explosion, and he did this in 1985 >or 1986.
It is a new result. Dawson's paper is in Math. Mag. 57(1):27-30 (1984). He constructed a collection of convex objects arranged so that no single object could be translated without disturbing the others. It turns out that 21 years earlier, Fejes-Toth and Heppes established a somewhat stronger result. But for both of their examples, it is still possible to separate the objects if one permits moving a collection of several objects at once in unison. And it is this that Snoeyink and Stolfi showed is not always possible.