RotationMatrix Applying

RGS[n_,m_]:=Module[{rt,rm},
rt=RandomReal[{-1,1},{n,2}];rm=RotationMatrix[Pi/m];
Graphics[{Opacity[.4],Style[Polygon[rt.MatrixPower[rm,#]],
ColorData["BrightBands"][1-#/(2m)]]&/@Range[2m]},
Background->RGBColor["silver"],ImageSize->600]];
  RGS[128,6]