On convex polygons and their complements as images of regular and polynomial maps of R2

In this work, we continue the study of polynomial and regular images of Euclidean spaces initiated in recent papers by Fernando and Gamboa. We prove that the complement of each convex polygon in R2 distinct of a band, and the complement of its interior, are images of polynomial maps R2→R2. We also represent each convex polygon and its interior as regular images of R2.