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Lattice-Width Directions and Minkowski's $3^d$-Theorem
2012
SIAM Journal on Discrete Mathematics
Preserved Fulltext
We show that the number of lattice directions in which a 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 Minkowski.
doi:10.1137/120877635
fatcat:7ouya3fppvbuzpcwaydqnt744q