, Volume 12, Issue 2, pp 237–240 | Cite as

Note dual polytopes of rational convex polytopes

  • Takayuki Hibi


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 polytopePdual ofP to be integral is presented.

AMS Subject Classification code (1991)

52 B 20 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    B. Grünbaum:Convex Polytopes, John Wiley & Sons, Inc., New York, N.Y., 1967.zbMATHGoogle Scholar
  2. [2]
    T. Hibi: A combinatorial self-reciprocity theorem for Ehrhart quasi-polynomials of rational convex polytopes,European J. Combinatorics, to appear.Google Scholar
  3. [3]
    R. Stanley:Enumerative Combinatorics, Volume I, Wadsworth, Monterey, Calif., 1986.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó 1992

Authors and Affiliations

  • Takayuki Hibi
    • 1
  1. 1.Department of Mathematics Faculty of ScienceHokkaido UniversitySapporo 060Japan

Personalised recommendations