GraphicsGrid[

 Partition[

  Table[With[{pts = Table[i {Cos[8/n i], Sin[8/n i]}, {i, n}]}, 

    Graphics[{Green, Line[pts], Red, Point[pts], Thick, Black, 

      BezierCurve[pts, SplineDegree -> (n - 1)]}, 

     PlotLabel -> Row[{"degree ", n - 1}]]], {n, 4, 16}], 4], 

 Frame -> All, ImageSize -> {500, 500}]