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Cutting a polytope

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Abstract

We investigate whether it is the case that for every convexd-polytopeP and pair of distinct verticesx andy ofP, there exists a hyperplane passing throughx andy which cutsP into two smallerd-polytopes, one of which has fewer facets thanP. Such a result would lead to inductive proofs of Conjectures 1 and 2 below. However, ford≥4, our answer is in the negative.

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Authors and Affiliations

  1. University of Michigan, 48109, Ann Arbor, MI, USA

    William Jockusch

  2. Purdue University, 47907, West Lafayette, IN, USA

    Nagabhushana Prabhu

Authors
  1. William Jockusch
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  2. Nagabhushana Prabhu
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Jockusch, W., Prabhu, N. Cutting a polytope. Geom Dedicata 54, 307–312 (1995). https://doi.org/10.1007/BF01265345

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