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We study the plastic crystal phase and chiral phase of hard regular polygons using Monte Carlo computer simulation. We establish predictive rules associating the number of sides of polygons to their phase behaviors. These rules could guide the design and selection of building blocks to achieve desired orientational ordering patterns in their assembled structure. In addition, we confirm the existence of a chiral phase in hard equilateral triangle system and discover a similar chiral phase in hard square system. Our study of the evolution of chirality suggests that the chiral transition is continuous. Knowledge gained from this study could contribute to the design of scalable fabrication based on spontaneous symmetry breaking to obtain materials with unique chirality with desirable optical properties.