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Polytopes with centrally symmetric faces

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Abstract

It is shown that if, for some 2≦j≦d-2, all thej-faces of ad-polytopeP are centrally symmetric, then all the faces ofP of every dimension are centrally symmetric.

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References

  1. A. D. Aleksandrov,A theorem on convex polyhedra, Trudy Mat. Inst. Steklov,4 (1933), 87. (Russian.)

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  2. B. Grünbaum,Convex Polytopes, John Wiley and Sons, London-New York-Sydney, 1967.

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  3. G. C. Shephard,Polytopes with centrally symmetric faces, Canad. J. Math.,19 (1967), 1206–1213.

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Authors and Affiliations

  1. Michigan State University, East Lansing, Michigan

    P. McMullen

  2. University College, London

    P. McMullen

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  1. P. McMullen
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McMullen, P. Polytopes with centrally symmetric faces. Israel J. Math. 8, 194–196 (1970). https://doi.org/10.1007/BF02771315

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  • DOI: https://doi.org/10.1007/BF02771315

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