Finite Möbius Groups
The purpose of this introductory section is to classify all finite isometry groups G acting on R3. Restricting ourselves first to direct (orientation preserving) isometries, using a Burnside counting argument, we will prove a result of Klein  asserting that a finite group G of direct isometries of R3 is either cyclic, dihedral, or the symmetry group of a Platonic solid. We finish this section augmenting G by opposite (orientation reversing) isometries. The main reference for this section is Coxeter .
KeywordsGalois Group Linear Fractional Transformation Finite Subgroup Minimal Immersion Platonic Solid
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