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Polytopes with Preassigned Automorphism Groups

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Abstract

We prove that every finite group is the automorphism group of a finite abstract polytope isomorphic to a face-to-face tessellation of a sphere by topological copies of convex polytopes. We also show that this abstract polytope may be realized as a convex polytope.

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Acknowledgments

The authors would like to thank Branko Grünbaum for providing useful comments during the preparation of this paper; Tom Tucker for some helpful discussion about group actions on maps; and finally the referees for making valuable suggestions that have improved the paper. The first author was supported by NSA-grant H98230-14-1-0124.

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Authors and Affiliations

  1. Department of Mathematics, Northeastern University, Boston, MA, 02115, USA

    Egon Schulte

  2. Department of Mathematics and Statistics, University of Alaska Fairbanks, Fairbanks, AK, 99709, USA

    Gordon Ian Williams

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  1. Egon Schulte
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  2. Gordon Ian Williams
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Correspondence to Gordon Ian Williams.

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Schulte, E., Williams, G.I. Polytopes with Preassigned Automorphism Groups. Discrete Comput Geom 54, 444–458 (2015). https://doi.org/10.1007/s00454-015-9710-1

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  • DOI: https://doi.org/10.1007/s00454-015-9710-1

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