We consider the set S of triples (x,y,z) corresponding tot he frequency of each alphabet letter in some infinite ternary square free word (so x + y + z = 1). We conjecture that this set is convex. We obtain bounds on S by whith a ganaralization of our method to bound the extremal frequency of one letter. This method uses weights on the alphabet letters. Finally, we obtain positive results, that is, explicit triples in S lying close to its boundary.