The reconstructions of the 6H-SiC(0001) surface under both Si-rich and C-rich conditions were studied using field ion-scanning tunneling microscopy (FI-STM). The sample was cleaned by in situ Si beam etching at 900-1000 degrees C. The as-cleaned surface showed a (root 3 x root 3) structure. The Si-rich phases were produced by annealing the sample in a Si flux, With increasing Si concentration, (2 x 2), (2 root 3 x 6 root 3), (3 x 3), and (7 x 7) reconstructions Were observed. Reaction of the Si-rich phases with C2H2 molecules at 1050 degrees C resulted in the formation of a C-rich surface, which exhibited a (2 x 2 )/(6 x 6) reconstruction. A structure model for (root 3 x root 3) reconstruction is proposed, and possible applications of using the surface reconstruction to selectively grow SIC polytype is discussed.