  We consider noncommuting pairs P,Q of intermediate subfactors of an
irreducible, finite-index inclusion N in M of II_1 factors such that P and Q
are supertransitive with Jones index less than 4 over N. We show that up to
isomorphism of the standard invariant, there is a unique such pair
corresponding to each even value [P:N]=4cos^2(pi/2n) but none for the odd
values [P:N]=4cos^2 (pi/(2n+1)).
  We also classify the angle values which occur between pairs of intermediate
subfactors with small index over their intersection: if [P:N] < 4, then the
unique nontrivial angle value is always cos^-1 (1/([P:N]-1)).

Operator Algebras