  We investigate a three-dimensional kinetically-constrained model that
exhibits two types of phase transitions at different densities. At the jamming
density $ \rho_J $ there is a mixed-order phase transition in which a finite
fraction of the particles become frozen, but the other particles may still
diffuse throughout the system. At the caging density $ \rho_C > \rho_J $, the
mobile particles are trapped in finite cages and no longer diffuse. The caging
transition occurs due to a percolation transition of the unfrozen sites, and we
numerically find that it is a continuous transition with the same critical
exponents as random percolation.
