Prove that there exist $2001$ convex polyhedra such that any three of them do not have any common points but any two of them touch each other (i.e., have at least one common boundary point but no common inner points).
Source: ToT - 2001 Spring Senior A-Level #6
Tags: geometry unsolved, geometry
Prove that there exist $2001$ convex polyhedra such that any three of them do not have any common points but any two of them touch each other (i.e., have at least one common boundary point but no common inner points).