  Consider a convex polygon P in the plane, and denote by U a homothetical copy
of the vector sum of P and (-P). Then the polygon U, as unit ball, induces a
norm such that, with respect to this norm, P has constant Minkowskian width. We
define notions like Minkowskian curvature, evolutes and involutes for polygons
of constant U-width, and we prove that many properties of the smooth case,
which is already completely studied, are preserved. The iteration of involutes
generates a pair of sequences of polygons of constant width with respect to the
Minkowski norm and its dual norm, respectively. We prove that these sequences
are converging to symmetric polygons with the same center, which can be
regarded as a central point of the polygon P.
