g1[x_]:=−3/2*Im[x*(1−x^4)/(x^6+Sqrt[5]*x^3−1)]

g2[x_]:=−3/2*Re[x*(1+x^4)/(x^6+Sqrt[5]*x^3−1)]

g3[x_]:=Im[(1+x^6)/(x^6+Sqrt[5]*x^3−1)]−1/2

x[x_]:=g1[x]/(g1[x]^2+g2[x]^2+g3[x]^2)

y[x_]:=g2[x]/(g1[x]^2+g2[x]^2+g3[x]^2)

z[x_]:=g3[x]/(g1[x]^2+g2[x]^2+g3[x]^2)

w[r_,f_]:=r*(Cos[f]+I*Sin[f])

ParametricPlot3D[{x[w[r,f]],y[w[r,f]],z[w[r,f]]},{r,0,1},{f,0,2*Pi},Mesh->{40,80},MeshStyle->Opacity[0.2],PlotRange->Automatic,Boxed->False,Axes->False, Background->Black,PlotStyle->Opacity[1]]

ParametricPlot3D[{x[w[r,f]],y[w[r,f]],z[w[r,f]]},{r,0,1},{f,0,2*Pi},Mesh->{40,80},MeshStyle->Opacity[0.2],PlotRange->Automatic,Boxed->False,Axes->False, Background->Black,PlotStyle->Opacity[0.2]]