Abstract
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].
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© 2002 Springer Science+Business Media New York
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Toth, G. (2002). Finite Möbius Groups. In: Finite Möbius Groups, Minimal Immersions of Spheres, and Moduli. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0061-8_1
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DOI: https://doi.org/10.1007/978-1-4613-0061-8_1
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6546-7
Online ISBN: 978-1-4613-0061-8
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