Distance between vertices of lattice polytopes
Résumé
A lattice (d, k)-polytope is the convex hull of a set of points in dimension d whose coordinates are integers ranging between 0 and k. We consider the largest possible distance δ (d, k) between two vertices in the edge-graph of a lattice (d, k)-polytope. We show that δ (5, 3) and δ (3, 6) are equal to 10. This substantiates the conjecture whereby δ (d, k) is achieved by a Minkowski sum of lattice vectors.
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