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A theorem on cyclic polytopes

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Abstract

LetC(ν, d) represent a cyclic polytope withν vertices ind dimensions. A criterion is given for deciding whether a given subset of the vertices ofC(ν, d) is the set of vertices of some face ofC(ν, d). This enables us to determine, in a simple manner, the number ofj-faces ofC(ν, d) for each value ofj (1≦j≦d−1).

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References

  1. C. Carathéodory,Ueber den Variabilitätsbereich der Koeffizienten von Potentzreiher die gegebene Werte nicht annehmen, Math. Ann.64 (1907), 95–115.

    Article  MathSciNet  MATH  Google Scholar 

  2. C. Carathéodory,Ueber den Variabilitätsbereich der Fourierschen Konstanten von positiven harmonischen Funktionen Rend. Circ. Mat. Palermo,32 (1911), 193–217.

    MATH  Google Scholar 

  3. D. Gale,Neighborly and cyclic polytopes, Proc. Symp. Pure Math.,7 (Convexity) (1963), 225–232.

    MathSciNet  Google Scholar 

  4. B. Grünbaum,Convex Polytopes, London-New York-Sydney, 1967.

  5. T. S. Motzkin,Comonotone curves and polyhedra, Abstract Bull. Am. Math. Soc.,63 (1957), 35.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. University of East Anglia, Nor 88C, Norwich, England

    G. C. Shephard

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  1. G. C. Shephard
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Shephard, G.C. A theorem on cyclic polytopes. Israel J. Math. 6, 368–372 (1968). https://doi.org/10.1007/BF02771216

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  • DOI: https://doi.org/10.1007/BF02771216

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