Lattice-width directions and Minkowski's 3^d-theorem

J. Draisma, T.B. McAllister, B. Nill

Research output: Contribution to journalArticleAcademicpeer-review

6 Citations (Scopus)
148 Downloads (Pure)


We show that the number of lattice directions in which a d-dimensional convex body in R^d has minimum width is at most 3^d-1, with equality only for the regular cross-polytope. This is deduced from a sharpened version of the 3^d-theorem due to Hermann Minkowski (22 June 1864--12 January 1909), for which we provide two independent proofs.
Original languageEnglish
Pages (from-to)1104-1107
JournalSIAM Journal on Discrete Mathematics
Issue number3
Publication statusPublished - 2012


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