This paper reports fundamental research on the general conditions for railway wheel polygonal wear to evolve. A common workflow for prediction of railway wheel polygonization is presented including assumptions, simulation scheme, and wear models. Based on this workflow, some rules for the evolution of railway wheel polygonization are proposed providing innovative perspectives to understand the basic mechanism of railway wheel polygonization. After summarising these rules, the general conditions for railway wheel polygonal wear to evolve are established. The phase between the instantaneous wear depth and the excitation is the key indicator determining the wheel OOR (Out-Of-Roundness) evolution direction (to grow or to diminish). The evolution tendency curve obtained from the instantaneous wear FRF (Frequency Response Function) is a useful tool to predict the OOR evolution, especially for predicting the OOR order that would grow predominantly at a given speed. If one or more structural modes can dominate the evolution tendency curve, and the energy distribution of track excitation allows this/these structural modes to be excited effectively, corresponding OOR orders can occur dominantly.