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Subpolytopes of stack polytopes

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Abstract

A polytopeP is called asubpolytope of a polytopeQ if vertP ⊆ vertQ. The purpose of this paper is to construct examples of 3-dimensional polytopes which are not subpolytopes of stack polytopes. Previously no such examples were known.

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Authors and Affiliations

  1. University of East Anglia, NR4 7TJ, Norwich, England

    G. C. Shephard

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  1. G. C. Shephard
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Additional information

For the properties of convex polytopes and an explanation of the standard terminology and notation used here, see B. Grünbaum,Convex Polytopes, London-New York-Sydney, 1967, or P. McMullen and G. C. Shephard,Convex Polytopes and the Upper Bound Conjecture, London Mathematical Society Lecture Note Series Volume 3, Cambridge, 1971.

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Shephard, G.C. Subpolytopes of stack polytopes. Israel J. Math. 19, 292–296 (1974). https://doi.org/10.1007/BF02757728

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  • DOI: https://doi.org/10.1007/BF02757728

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