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Infinite series of combinatorially regular polyhedra in three-space

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Abstract

The paper discusses polyhedral realizations in ordinary Euclidean 3-space of Coxeter's regular skew polyhedra {4, p|4p/2]−1} and their duals on an orientable surface of genus 2p−3(p−4)+1. Our considerations are based on work of Coxeter, Ringel and McMullen et al., revealing that certain polyhedral manifolds discovered by the last three authors are in fact the polyhedra in question. We also describe Kepler-Poinsot-type polyhedra in 3-space obtained by projections from Coxeter's regular skew star-polyhedra in 4 dimensions.

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References

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Authors and Affiliations

  1. Department of Mathematics, University College London, WC1E 6BT, London, UK

    P. McMullen

  2. Math. Inst. Univ. Dortmund, Neubau Math., D-4600, Dortmund 50, Germany

    E. Schulte

  3. Math. Inst. Univ. Siegen, Hoelderlinstr. 3, D-5900, Siegen, Germany

    J. M. Wills

Authors
  1. P. McMullen
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  2. E. Schulte
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  3. J. M. Wills
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McMullen, P., Schulte, E. & Wills, J.M. Infinite series of combinatorially regular polyhedra in three-space. Geom Dedicata 26, 299–307 (1988). https://doi.org/10.1007/BF00183021

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  • DOI: https://doi.org/10.1007/BF00183021

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