A smooth plane is a flat surface that is even and free of any bumps or irregularities. Synonyms for this word might include "flattened," "leveled," or "polished." Other possibilities could include "sanded," "buffed," or "refined." Depending on the context, additional synonyms might be appropriate. For example, in a woodworking context, "planed" or "jointed" could be good alternatives. In a scientific context, "optically flat" might be a useful synonym. Regardless of the specific phrasing, the underlying meaning remains the same: a smooth plane is a surface that is uniform and regular, providing a stable foundation for whatever activity is taking place on top of it.