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Convex polytopes without triangular faces

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Abstract

LetP be a convexd-polytope without triangular 2-faces. Forj=0,…,d−1 denote byf j(P) the number ofj-dimensional faces ofP. We prove the lower boundf j(P)≥f j(C d) whereC d is thed-cube, which has been conjectured by Y. Kupitz in 1980. We also show that for anyj equality is only attained for cubes. This result is a consequence of the far-reaching observation that such polytopes have pairs of disjoint facets. As a further application we show that there exists only one combinatorial type of such polytopes with exactly 2d+1 facets.

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Authors and Affiliations

  1. Math. Institut B, Universität Stuttgart, Pfaffenwaldring 57, D7000, Stuttgart 80, FRG

    G. Blind

  2. Waldburgstr. 88, D7000, Stuttgart 80, FRG

    R. Blind

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  1. G. Blind
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  2. R. Blind
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Blind, G., Blind, R. Convex polytopes without triangular faces. Israel J. Math. 71, 129–134 (1990). https://doi.org/10.1007/BF02811879

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  • DOI: https://doi.org/10.1007/BF02811879

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