,t)=-2</code> if <code>m(s,t)=‚àû</code>. Then the action of <code>s‚àà S</code> on <code>V</code> is given by <code>s(e‚Çú)=e‚Çú-C(s,t)e‚Çõ</code>.</p><p>Thus, Coxeter groups are  real reflection groups.  The converse need not be true  if the set of reflecting  hyperplanes has bad topological properties, but  it turns out  that finite Coxeter  groups are the  same as finite real reflection  groups. The possible Coxeter matrices for finite Coxeter groups have  been  completely  classifie