Glass formers are characterized by their ability to avoid crystallization. As monodisperse systems tend to rapidly crystallize, the most common glass formers in simulations are systems composed of mixtures of particles with different sizes. Here, we make use of the ability of patchy particles to change their local structure to propose them as monodisperse glass formers. We explore monodisperse systems with two patch geometries: a 12-patch geometry that enhances the formation of icosahedral clusters and an 8-patch geometry that does not appear to strongly favor any particular local structure. We show that both geometries avoid crystallization and present glassy features at low temperatures. However, the 8-patch geometry better preserves the structure of a simple liquid at a wide range of temperatures and packing fractions, making it a good candidate for a monodisperse glass former.