An important class of Coxeter groups are the finite ones, like above. One can show that a
Coxeter group is finite if and only if the scalar product defined by Equation (3.28) on is
Euclidean [107]. Finite Coxeter groups coincide with finite reflection groups in Euclidean space
(through hyperplanes that all contain the origin) and are discrete subgroups of . The
classification of finite Coxeter groups is known and is given in Table 1 for completeness. For finite
Coxeter groups, one has the important result that the Tits cone coincides with the entire space
[107].