We present the evidence of universality in conical tip formation during the freezing of arbitrary-shaped sessile droplets. The focus is to demonstrate the relationship between this universality and the liquid drop shape. We observe that, in the case of asymmetric drops, this universal shape is achieved when the tip reconfigures by changing its location, which subsequently alters the frozen drop shape. The proposed “two-triangle” model quantifies the change in the tip configuration as a function of the asymmetry of the drop that shows a good agreement with the experimental evidence. Finally, based on the experimental and theoretical exercise, we propose the scaling dependence between the variations in the tip configuration and the asymmetry of the drop.