In[]:=
ToReal[z_]:={Re[z],Im[z]};ToComplex[{x_,y_}]:=x+Iy;FrameToEdges[frame_]:=ToReal[ToComplex[#]^2]&/@Transpose[frame];FrameToVertices[frame_]:=Accumulate[FrameToEdges[frame]];DualFourFrame[frame_]:=Orthogonalize[NullSpace[frame]];Module[{frame,dualframe,n,cols},frame=Transpose[ToReal[Sqrt[#]]&/@Table[1/2E^(Iθ),{θ,0,2π-π/2,π/2}]];dualframe=DualFourFrame[frame];n=6;cols=RGBColor/@{"#FF6464","#FFBD67","#F8FE85","#5BE7A9"};Manipulate[Graphics[{FaceForm[None],Table[{EdgeForm[Directive[JoinForm["Round"],cols[[Mod[i,3,2]]],Thickness[.02]]],Polygon[FrameToVertices[Cos[t+iπ/n]frame+Sin[t+iπ/n]dualframe]]},{i,1,n}]},ImageSize->{540,540},Background->cols[[1]],PlotRange->{{-3/4,5/4},{-1,1}}],{t,0,π}]]