  For an isolated hypersurface singularity which is neither simple nor simple
elliptic, it is shown that there exists a distinguished basis of vanishing
cycles which contains two basis elements with an arbitrary intersection number.
This implies that the set of Coxeter-Dynkin diagrams of such a singularity is
infinite, whereas it is finite for the simple and simple elliptic
singularities. For the simple elliptic singularities, it is shown that the set
of distinguished bases of vanishing cycles is also infinite. We also show that
some of the hyperbolic unimodal singularities have Coxeter-Dynkin diagrams like
the exceptional unimodal singularities.
