POPMN[m_,n_,k_,\[Theta]_]:=Cos[m*\[Theta]]+Cos[n*\[Theta]]+k;
PAPMN=Function[{m,n,k,t},
{(Cos[m*t]+Cos[n*t]+k+1)Cos[t],
(Cos[m*t]+Cos[n*t]+k+1)Sin[t]}];
CPMN=Function[{m,n,k,x,y},
x^2+y^2-(Cos[m*ArcTan[y/x]]+Cos[n*ArcTan[y/x]]+k+2)^2];
S3P=Function[{m,n,k,c1,c2,c3},
Show[PolarPlot[POPMN[m,n,k,\[Theta]],{\[Theta],0,2Pi},
PlotStyle->ColorData[c1][1-.1k]],
ParametricPlot[PAPMN[m,n,k,t],{t,0,2Pi+.1},
PlotStyle->ColorData[c2][1-.3k]],
ContourPlot[CPMN[m,n,k,x,y]==0,{x,-6,6},{y,-6,6},
ContourStyle->ColorData[c3][1-.5k]],
Axes->False,ImageSize->500,Frame->True]];
S3P[24,12,2,"RoseColors","AvocadoColors","NeonColors"]