  A hollow axis-aligned box is the boundary of the cartesian product of $d$
compact intervals in R^d. We show that for d\geq 3, if any 2^d of a collection
of hollow axis-aligned boxes have non-empty intersection, then the whole
collection has non-empty intersection; and if any 5 of a collection of hollow
axis-aligned rectangles in R^2 have non-empty intersection, then the whole
collection has non-empty intersection. The values 2^d for d\geq 3 and 5 for d=2
are the best possible in general. We also characterize the collections of
hollow boxes which would be counterexamples if 2^d were lowered to 2^d-1, and 5
to 4, respectively.
