The melting transition of two-dimensional (2D) systems is a fundamental problem in condensed matter and statistical physics that has advanced significantly through the application of computational resources and algorithms. 2D systems present the opportunity for novel phases and phase transition scenarios not observed in 3D systems, but these phases depend sensitively on the system and thus predicting how any given 2D system will behave remains a challenge. Recently we carried out a comprehensive simulation study of the phase behavior near the melting transition of all hard regular polygons with 3 ≤ n ≤ 14 vertices using massively parallel Monte Carlo simulations of up to one million particles. By investigating this family of shapes, we can show that the melting transition depends upon both particle shape and symmetry considerations, which together can predict which of three different melting scenarios will occur for a given n.