29 Apr
2013
29 Apr
'13
9:18 p.m.
David Makin <makinmagic@tiscali.co.uk> wrote:
I meant such that the "countries" are volumes not surfaces - and I suspect the answer is 5 (based on change from triangle to tetrahedron).
No, the answer is unbounded. For instance let each 3D country consist of a wide horizontal plate with a long vertical rod attached. You can stack any number of plates, and they all touch each other. (The plates have holes just big enough for the rods to snugly fit through.) But I wonder what the answer is if the countries are constrained to be convex. Probably still unbounded, given that all graphs are embeddable in three-space, but my geometric intuition isn't good enough to be sure of this.