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Chiral Polytopes and Suzuki Simple Groups

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Rigidity and Symmetry

Part of the book series: Fields Institute Communications ((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 < G ≤ Aut(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.

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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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Authors and Affiliations

  1. Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, Mexico City D.F., 04510, México

    Isabel Hubard

  2. Department of Mathematics, University of Auckland, 92019, Auckland, New Zealand

    Dimitri Leemans

Authors
  1. Isabel Hubard
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  2. Dimitri Leemans
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Correspondence to Dimitri Leemans .

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Editors and Affiliations

  1. Department of Mathematics, Cornell University, Ithaca, New York, USA

    Robert Connelly

  2. Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada

    Asia Ivić Weiss

  3. Department of Mathematics & Statistics, York University, Toronto, Ontario, Canada

    Walter Whiteley

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Hubard, I., Leemans, D. (2014). Chiral Polytopes and Suzuki Simple Groups. In: Connelly, R., Ivić Weiss, A., Whiteley, W. (eds) Rigidity and Symmetry. Fields Institute Communications, vol 70. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0781-6_9

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