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
B. Grünbaum:Convex Polytopes, John Wiley & Sons, Inc., New York, N.Y., 1967.
T. Hibi: A combinatorial self-reciprocity theorem for Ehrhart quasi-polynomials of rational convex polytopes,European J. Combinatorics, to appear.
R. Stanley:Enumerative Combinatorics, Volume I, Wadsworth, Monterey, Calif., 1986.
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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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DOI: https://doi.org/10.1007/BF01204726