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}]