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Chiral Polytopes and Suzuki Simple Groups

  • Isabel Hubard
  • Dimitri LeemansEmail author
Chapter
Part of the Fields Institute Communications book series (FIC, volume 70)

Abstract

For each q ≠ 2 an odd power of 2, we show that the Suzuki simple group S = Sz(q) is the automorphism group of considerably more chiral polyhedra than regular polyhedra. Furthermore, we show that S cannot be the automorphism group of an abstract chiral polytope of rank greater than 4. For each almost simple group G such that S < GAut(S), we prove that G is not the automorphism group of an abstract chiral polytope of rank greater than 3, and produce examples of chiral 3-polytopes for each such group G.

Keywords

Abstract chiral polytopes Suzuki simple groups 

Subject Classifications

52B11 20D06 

Notes

Acknowledgements

We would like to thank the Fields Institute for the support we received during the Discrete Geometry and Applications Thematic Program, part of this work was done when the authors visited the Institute. We also gratefully acknowledge financial support of “PAPIIT – México (Grant IN106811)” the “Fonds David et Alice Van Buuren” and the “Communauté Française de Belgique – Action de Recherche Concertée” for this project. Finally, we thank the referee for the careful reading of our paper and the suggestions to improve this paper.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Instituto de MatemáticasUniversidad Nacional Autónoma de MéxicoMexico City D.F.México
  2. 2.Department of MathematicsUniversity of AucklandAucklandNew Zealand

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