Finite Möbius Groups

  • Gabor Toth
Part of the Universitext book series (UTX)


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 [1] 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 [2].


Galois Group Linear Fractional Transformation Finite Subgroup Minimal Immersion Platonic Solid 
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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Gabor Toth
    • 1
  1. 1.Department of Mathematical SciencesRutgers University, CamdenCamdenUSA

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