Let G ⊆ SO 3 ( R ) {\displaystyle {}G\subseteq \operatorname {SO} _{3}\!{\left(\mathbb {R} \right)}} be a finite subgroup of order n {\displaystyle {}n} of the group of proper, linear isometries of R 3 {\displaystyle {}\mathbb {R} ^{3}} . Let K 1 , … , K m {\displaystyle {}K_{1},\ldots ,K_{m}} be the different classes of semiaxes of G {\displaystyle {}G} , and for every class, let n i {\displaystyle {}n_{i}} , i = 1 , … , m {\displaystyle {}i=1,\ldots ,m} , be the order of the stabilizer group G H {\displaystyle {}G_{H}} , H ∈ K i {\displaystyle {}H\in K_{i}} , which are, due to fact, independent of H ∈ K i {\displaystyle {}H\in K_{i}} .
