Corona limits of tilings : Periodic case

We study the limit shape of successive coronas of a tiling, which models the growth of crystals. We define basic terminologies and discuss the existence and uniqueness of corona limits, and then prove that corona limits are completely characterized by directional speeds. As an application, we give another proof that the corona limit of a periodic tiling is a centrally symmetric convex polyhedron (see [Zhuravlev 2001], [Maleev-Shutov 2011]).