The geometry of polymeric hollow fibers for hemodialysis or desalination is a key factor determining their performance. Deformations are frequently observed, but they are rather random. Here we were able to exactly control the shape evolution of the internal channels or lumens of polymeric hollow fibers, leading to polygonal geometries with increasing number of sides. The elasticity of the incipient channel skin and instabilities during fiber formation are affected by the internal coagulant fluid composition and flow rate; and highly influence the polygonal shape. We propose a holistic explanation by analyzing the thermodynamic, kinetic and rheological aspects involved in the skin formation and their synergy.