A new algorithm to classify chiral polytopes with a given automorphism group

Abstract

We present a new algorithm to compute all the chiral polytopes that have a given group as full automorphism group. This algorithm uses a new set of generators that characterize the group, all of them except one being involutions. It permits to compute all chiral polytopes of groups that were previously unreachable by other known algorithms.

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Notes

  1. 1.

    See https://www.math.auckland.ac.nz/~conder/.

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Acknowledgements

The authors would like to thank an anonymous referee for fruitful comments on a preliminary version of this paper.

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Correspondence to Francis Buekenhout.

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Buekenhout, F., Leemans, D. & Tranchida, P. A new algorithm to classify chiral polytopes with a given automorphism group. Beitr Algebra Geom (2021). https://doi.org/10.1007/s13366-020-00536-1

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Keywords

  • Chiral polytopes
  • \(C^+\)-groups
  • Hypertopes