  Boundary critical phenomena are studied in the 3- State Potts model in 2
dimensions using conformal field theory, duality and renormalization group
methods. A presumably complete set of boundary conditions is obtained using
both fusion and orbifold methods. Besides the previously known free, fixed and
mixed boundary conditions a new one is obtained. This illustrates the necessity
of considering fusion with operators that don't occur in the bulk spectrum, to
obtain all boundary conditions. It is shown that this new boundary condition is
dual to the mixed ones. The phase diagram for the quantum chain version of the
Potts model is analyzed using duality and renormalization group arguments.
