Self-Packing of Minkowski Disks.

A Minkowski disk is the unit ball of a 2-dimensional Minkowski space, i.e., a compact convex body symmetric around 0 in R sup 2 which has nonempty interior. The self-packing radius p (m,B) is the smallest t such that tB can be packed with m translates of B. For m = 6 we show that the self-packing radius p(m,B) = 1 + 2 over alpha (m,B) where alpha (m,B) is the Minkowski length of the side of the largest equilateral m-gon inscribed in B (measured in the Minkowski metric determined by B).