Editing 3D rotation group (section)

===Complete classification of finite subgroups===
The finite subgroups of <math>\mathrm{SO}(3)</math> are completely [[classification theorem|classified]].<ref name="coxeter">{{cite book |last1=Coxeter |first1=H. S. M. |title=Regular polytopes |date=1973 |location=New York |isbn=0-486-61480-8 |page=53 |edition=Third}}</ref>

Every finite subgroup is isomorphic to either an element of one of two [[countably infinite]] families of planar isometries: the [[cyclic group]]s <math>C_n</math> or the [[dihedral group]]s <math>D_{2n}</math>, or to one of three other groups: the [[tetrahedral group]] <math>\cong A_4</math>, the [[octahedral group]] <math>\cong S_4</math>, or the [[icosahedral group]] <math>\cong A_5</math>.