As we saw in Chapter 2, the description of all finite subgroups of O(R 3) is rather involved. The enumeration of finite subgroups of O(V) becomes considerably more involved when V has dimension greater than 3. When n = 4 the subgroups are discussed in ; complete listings are known for only a few small values of n. Thus we limit our discussion at this point to the primary subject of the book—the important class of finite subgroups of O(V)that are generated by reflections.
KeywordsRoot System Coxeter Group Dual Basis Dihedral Group Finite Subgroup
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