ABSTRACT
A Minkowski space Md =(Rd , || ||) is just Rd with distances measured using a norm || ||. A norm || || is completely determined by its unit ball
which is a compact convex set with nonempty interior (i.e. a convex body), centrally symmetric about the origin o in Rd . An elegant result of Petty [15] claims that the cardinality of any equilateral set in Md is at most 2 d i.e. the cardinality of any family of pairwise different translates of the unit ball B in Md such that any two translates are tangent is at most 2 d . Motivated by this result and the results in [3] and [17] we introduce the following definitions.
