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Phase behaviors of two-dimensional (2D) systems constitute a fundamental topic in condensed matter and statistical physics. Although hard polygons and interactive point-like particles are well studied, the phase behaviors of more realistic molecular systems considering intermolecular interaction and molecular shape remain elusive. Here we investigate by molecular dynamics simulation thermal stabilities of 2D ball-stick polygons, serving as simplified models for molecular systems. Below the melting temperature $T_{m}$, we identify a critical edge number $n_{c}$, at which a waving superlattice structure emerges; when n < $n_{c}$,the triangular system stabilizes at a spin-ice-like glassy state; when n > $n_{c}$,the polygons stabilize at crystalline states, and $T_{m}$ is higher for polygons with more edges at higher pressures but exhibits a crossover for hexagon and octagon at low pressures. A theoretical framework taking into account the competition between entropy and enthalpy is proposed to provide a comprehensive understanding of our results, which is anticipated to facilitate the design of 2D materials., Comment: Version 4 is accepted by Nature Communications