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Neighborly cubical polytopes and spheres

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Abstract

We prove that the neighborly cubical polytopes studied by Günter M. Ziegler and the first named author [14] arise as a special case of the neighborly cubical spheres constructed by Babson, Billera and Chan [4]. By relating the two constructions we obtain an explicit description of a non-polytopal neighborly cubical sphere and, further, a new proof of the fact that the cubical equivelar surfaces of McMullen, Schulz and Wills [16] can be embedded into ℝ3.

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Authors and Affiliations

  1. Fachbereich Mathematik, AG 7, TU Darmstadt, 64289, Darmstadt, Germany

    Michael Joswig

  2. Institut für Mathematik, MA 6-2, TU Berlin, 10623, Berlin, Germany

    Thilo Rörig

Authors
  1. Michael Joswig
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  2. Thilo Rörig
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Additional information

Both authors are supported by Deutsche Forschungsgemeinschaft, DFG Research Group “Polyhedral Surfaces.”

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Joswig, M., Rörig, T. Neighborly cubical polytopes and spheres. Isr. J. Math. 159, 221–242 (2007). https://doi.org/10.1007/s11856-007-0044-4

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  • DOI: https://doi.org/10.1007/s11856-007-0044-4

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