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Realizations of regular apeirotopes

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Summary

In an earlier paper, a theory of realizations of (finite) regular polytopes in euclidean spaces was developed. Here, the analogous problem of realizing regular apeirotopes (infinite polytopes) is investigated. While no complete theory is expounded, several basic results are established. Among these is the curious fact that, if a regular apeirotope has a discrete realization, then it has one with no translations in its symmetry group.

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Authors and Affiliations

  1. Department of Mathematics, University College London, Gower Street, WC1E 6BT, London, England

    Peter McMullen

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  1. Peter McMullen
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McMullen, P. Realizations of regular apeirotopes. Aeq. Math. 47, 223–239 (1994). https://doi.org/10.1007/BF01832961

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  • DOI: https://doi.org/10.1007/BF01832961

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