Abstract: Electron vortex beams hold great promise for development in transmission electron microscopy but have yet to be widely adopted. This is partly due to the complex set of interactions that occur between a beam carrying orbital angular momentum (OAM) and a sample. Herein, the system is simplified to focus on the interaction between geometrical symmetries, OAM, and topology. We present multiple simulations alongside experimental data to study the behavior of a variety of electron vortex beams after interacting with apertures of different symmetries and investigate the effect on their OAM and vortex structure, both in the far field and under free-space propagation.