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McMullen's conditions and some lower bounds for general convex polytopes

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Abstract

We give a lower bound for the number of vertices of a generald-dimensional polytope with a given numberm ofi-faces for eachi = 0,..., ⌎d/2⌏ − 1. The tightness of those bounds is proved using McMullen's conditions. Form greater than a small constant, those lower bounds are attained by simpliciali-neighbourly polytopes.

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Authors and Affiliations

  1. Department of Information Sciences, Tokyo Institute of Technology, 2-12-1 Ohokayama, Meguro-ku, 152, Tokyo, Japan

    Antoine Deza

  2. centre d'Orsay, Université de Paris-sud, LRI, bât. 490, 91405, Paris Cedex, France

    Antoine Deza

  3. Graduate School of Systems Management, University of Tsukuba, 3-29-1 Otsuka, Bunkyo-ku, 112, Tokyo, Japan

    Komei Fukuda

Authors
  1. Antoine Deza
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  2. Komei Fukuda
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Deza, A., Fukuda, K. McMullen's conditions and some lower bounds for general convex polytopes. Geom Dedicata 52, 165–173 (1994). https://doi.org/10.1007/BF01263604

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  • DOI: https://doi.org/10.1007/BF01263604

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