Rotational twins are fundamental defects in III-V epitaxy, in particular for the growth on nonpolar (111) surfaces. Based on density functional theory (DFT) calculations, we develop a general model for III-V nucleation on vicinal non-polar (111)-oriented substrates and focus on the important differences in the atomic step configuration of different miscut directions. We verify this model by a relevant materials system when growing GaP epilayers on As-terminated Si(111): Scanning tunneling microscopy measurements reveal the formation of straight double bilayer steps after Aspassivation of the Si(111) surface, which persist after III-V growth, as we display when measuring the buried heterointerface with cross-sectional high-resolution transmission electron microscopy. A twin amount in the GaP epilayers is observed in dependence on the misorientation and our nucleation model explains the underlying mechanisms: The number of back-bonds at the step edges determines the nucleation site. Accordingly, the substrate misorientation towards [112] yields twin-suppression, which is in full agreement with experiment. Finally, we use DFT input for Kinetic Monte Carlo calculations to explain the formation of GaP rotational twins on Si(111):As in order to explain their volume fraction observed by high resolution X-ray diffraction measurements. We thus derive a complete picture of the formation and suppression of rotational twins relevant for low-defect III-V-on-Si integration.