  The three-dimensional $q$-state Potts model, forced into coexistence by
fixing the density of one state, is studied for $q=2$, 3, 4, and 6. As a
function of temperature and number of states, we studied the resulting
equilibrium droplet shapes. A theoretical discussion is given of the interface
properties at large values of $q$. We found a roughening transition for each of
the numbers of states we studied, at temperatures that decrease with increasing
$q$, but increase when measured as a fraction of the melting temperature. We
also found equilibrium shapes closely approaching a sphere near the melting
point, even though the three-dimensional Potts model with three or more states
does not have a phase transition with a diverging length scale at the melting
point.
