The permeability of a crystal mush fundamentally controls the ability of its melt to migrate or segregate with respect to the solid phase and thus controls the extent to which compaction and porous-media convection can occur in crystallizing igneous cumulates. In particular, the existence of a percolation threshold, which defines the porosity at which a crystallizing rock becomes impermeable, can limit the effectiveness of these processes. We present three-dimensional numerical models of the topology of porosity in both texturally equilibrated and nonequilibrated crystal-melt systems; these models enable porosity vs. permeability relationships and hence percolation thresholds to be calculated. The permeability of the nonequilibrated models was calculated using a network-simulation method. These models confirm that there is no percolation threshold for a perfectly texturally equilibrated rock with dihedral angles of <60°. Conversely, the models indicate that the percolation threshold for non–texturally equilibrated rocks is 8%–11%. The models show that permeability is only weakly dependent on the morphology of the crystals at porosities of >20%. These results suggest that the volume of trapped melt in an igneous cumulate may be controlled by the ability of the crystallizing crystal-melt system to reach textural equilibrium.