This paper presents the characterization and design aspects of a novel fabrication method that integrates photolithography and self-folding to create polymer polyhedral structures. A two-step UV exposure process is used to produce patterned polymer films with flexible folds of low cross-linking density and stiff faces of high cross-linking density. Solvent is diffused into the folds during the development step of the photolithography process due to their low cross-linking density. The solvent concentration is non-uniform across the thickness of the folds and causes a strain gradient at these regions when the solvent is removed by heating the films, which enables self-folding. Experiments are performed to calibrate an equation that relates the dimensions of the folds and their achieved fold angle. An analytical model is introduced to elucidate the form of the equation and provide physical meaning to the calibration parameter. The formula is incorporated into a computational implementation of the unfolding polyhedra method that considers smoothly bent folds. This method, enhanced with the experimentally calibrated formula, enables the design of planar films programmed to self-fold into target three-dimensional shapes when heated. Polyhedral shapes are fabricated to demonstrate the developed method for origami-based fabrication. A parametric study quantifying the accuracy of the designed polyhedral forms with smooth folds as compared against those with idealized creased folds is performed.