Note dual polytopes of rational convex polytopes

Combinatorica volume 12, pages237–240(1992)Cite this article

Abstract

LetP⊄ ℝd be a rational convex polytope with dimP=d such that the origin of ℝd is contained in the interiorP − ∂P ofP. In this paper, from a viewpoint of enumeration of certain rational points inP (which originated in Ehrhart's work), a necessary and sufficient condition for the dual polytopeP dual ofP to be integral is presented.

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References

  1. [1]

    B. Grünbaum:Convex Polytopes, John Wiley & Sons, Inc., New York, N.Y., 1967.

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    T. Hibi: A combinatorial self-reciprocity theorem for Ehrhart quasi-polynomials of rational convex polytopes,European J. Combinatorics, to appear.

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    R. Stanley:Enumerative Combinatorics, Volume I, Wadsworth, Monterey, Calif., 1986.

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Affiliations

  1. Department of Mathematics Faculty of Science, Hokkaido University, Kita-ku, Sapporo 060, Japan

    Takayuki Hibi

Authors
  1. Takayuki Hibi
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Additional information

This research was performed while the author was staying at Massachusetts Institute of Technology during the 1988–89 academic year.

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Hibi, T. Note dual polytopes of rational convex polytopes. Combinatorica 12, 237–240 (1992). https://doi.org/10.1007/BF01204726

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AMS Subject Classification code (1991)

  • 52 B 20