  This paper contains a complete description of minimal non-gatherable triangle
triples in the lambda-sequences for the classical root systems, $F_4$ and
$E_6$. Such sequences are associated with reduced decompositions (words) in
affine and non-affine Weyl groups. The existence of the non-gatherable triples
is a combinatorial obstacle for using the technique of intertwiners for an
explicit description of the irreducible representations of the (double) affine
Hecke algebras, complementary to their algebraic-geometric theory.
