All the conformal symmetry groups of the category C 2 can be derived as the extensions of the conformal symmetry groups of the category C 21 by the similarity transformations K , L , M . Therefore, every conformal symmetry rosette with a conformal symmetry group of the category C 2 can be constructed, multiplying by those similarity transformations a conformal symmetry rosette with the corresponding conformal symmetry group of the category C 21 . Developing our analysis further we will consider first the conformal symmetry groups of the category C 21 . They will be used to generate conformal symmetry groups of the category C 2 . That and similar problems can be solved in the same way as with the similarity symmetry groups S 20 .
Similar possibilities exist in all the other conformal symmetry groups.
There exists the possibility of varying the shape of boundaries that do not belong to reflection lines or inversion circles. Regaring the changes of the form of a fundamental region, conformal symmetry groups of the category C 2 offer similar possibilities as generating conformal symmetry groups of the category C 21 .