  We consider the division of a finite number of homogeneous divisible items
among three players. Under the assumption that each player assigns a positive
value to every item, we characterize the optimal allocations and we develop two
exact algorithms for its search. Both the characterization and the algorithm
are based on the tight relationship two geometric objects of fair division: the
Individual Pieces Set (IPS) and the Radon-Nykodim Set (RNS).
