There may be times when your polygon mesh does not appear as smooth as you would like. Maya provides several methods for smoothing polygons:
Troubleshooting the Smooth feature
Smooth works strangely or not at all?
Smoothing works with convex and even star-shaped concave faces. However, it can give unwanted results with concave faces where the center point is not inside the face.
To fix a concave faces, use Edit Mesh > Split Polygon Tool or Mesh > Triangulate.