  We consider the class of those Coxeter groups for which removing from the
Cayley graph any tubular neighbourhood of any wall leaves exactly two connected
components. We call these Coxeter groups bipolar. They include both the
virtually Poincare duality Coxeter groups and the infinite irreducible
2-spherical ones. We show in a geometric way that a bipolar Coxeter group
admits a unique conjugacy class of Coxeter generating sets. Moreover, we
provide a characterisation of bipolar Coxeter groups in terms of the associated
Coxeter diagram.
