Self-assembly of polyhedral-shaped particles has attracted huge interest with the advent of new synthesis methods that realize these faceted particles in the lab. Recent studies have shown that polyhedral-shaped particles exhibit a rich phase behavior by excluded volume interactions alone; some of these particles are even alleged to show a transition to a glass phase by quenching the liquid sufficiently fast beyond the glass transition (supercooling), such that the formation of structures with long-range order is suppressed. Despite the recent progress, no study has been made on the glass formation of polyhedral-shaped particles. Here, we study the glass behavior of polyhedral particles using advanced Monte Carlo methods. We investigate the formation of a glass of monodisperse hard polyhedral-shaped particles, namely, octahedra, tetrahedra, and triangular cupola, using simulations. Finally, the fragility of these particles is determined and compared to that of a polydisperse hard-sphere system.