Parametric Plotting Examples

r1=6; r2=9; R=12; n=24;
x=r1*Cos[t]-R*Cos[2i*\[Pi]/n]; y=r1*Sin[t]-R*Sin[4i*\[Pi]/n];
u=r2*Cos[t]-R*Cos[2i*\[Pi]/n]; v=r2*Sin[t]-R*Sin[2i*\[Pi]/n];
p1=ParametricPlot[Evaluate[Table[{x,y},{i,24}]],{t,0,2\[Pi]},
PlotStyle->Directive[Opacity[0.5],Blue]];
p2=ParametricPlot[Evaluate[Table[{y,x},{i,24}]],{t,0,2\[Pi]},
PlotStyle->ColorData[3,"ColorList"]];
p3=ParametricPlot[Evaluate[Table[{u,v},{i,24}]],{t,0,2\[Pi]},
PlotStyle->Directive[Opacity[0.5],Darker[Blue]]];
Show[p1,p2,p3,PlotRange->{{-21,21},{-21,21}},ImageSize->Large]