  The isomorphism problem for Coxeter groups has been reduced to its
'reflection preserving version' by B. Howlett and the second author. Thus, in
order to solve it, it suffices to determine for a given Coxeter system (W,R)
all Coxeter generating sets S of W which are contained in R^W, the set of
reflections of (W,R). In this paper, we provide a further reduction: it
suffices to determine all Coxeter generating sets S in R^W which are
sharp-angled with respect to R.
