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\documentclass[a4paper]{article}
\usepackage{pst-solides3d}
\pagestyle{empty}
\begin{document}
 
%@AUTEUR: Juergen Gilg
\psset[pst-solides3d]{viewpoint=10 9 15,SphericalCoor,
	Decran=40,lightsrc=5 5 10}
\begin{pspicture}(-6,-11)(-6,7)
\rput(0,0){
\defFunction[algebraic]{klein}(u,v){cos(u)*cos(v)/
    (-2.*sqrt(0.965/3.-0.935/3.*((cos(u)^4+sin(u)^4)*cos(v)^4+
    sin(v)^4))*cos((acos(-(-0.941/6.+0.374*((cos(u)^4+
    sin(u)^4)*cos(v)^4+sin(v)^4)-1.309/6.*((cos(u)^6+
    sin(u)^6)*cos(v)^6+sin(v)^6)-1.221*cos(u)^2*cos(v)^4*
    sin(u)^2*sin(v)^2)/sqrt(0.965/3.-0.935/3.*((cos(u)^4+
    sin(u)^4)*cos(v)^4+sin(v)^4))^3)+pi)/3.)+0.8)}%
{sin(v)/(-2.*sqrt(0.965/3.-0.935/3.*((cos(u)^4+sin(u)^4)*cos(v)^4+
    sin(v)^4))*cos((acos(-(-0.941/6.+0.374*((cos(u)^4+
    sin(u)^4)*cos(v)^4+sin(v)^4)-1.309/6.*((cos(u)^6+
    sin(u)^6)*cos(v)^6+sin(v)^6)-1.221*cos(u)^2*cos(v)^4*
    sin(u)^2*sin(v)^2)/sqrt(0.965/3.-0.935/3.*((cos(u)^4+
    sin(u)^4)*cos(v)^4+sin(v)^4))^3)+pi)/3.)+0.8)}%
{sin(u)*cos(v)/(-2.*sqrt(0.965/3.-0.935/3.*((cos(u)^4+
    sin(u)^4)*cos(v)^4+sin(v)^4))*cos((acos(-(-0.941/6.+0.374*((cos(u)^4+
    sin(u)^4)*cos(v)^4+sin(v)^4)-1.309/6.*((cos(u)^6+
    sin(u)^6)*cos(v)^6+sin(v)^6)-1.221*cos(u)^2*cos(v)^4*sin(u)^2*
    sin(v)^2)/sqrt(0.965/3.-0.935/3.*((cos(u)^4+sin(u)^4)*cos(v)^4+
    sin(v)^4))^3)+pi)/3.)+0.8)}
\psSolid[object=surfaceparametree,
    base=0 pi 2 mul  pi neg 2 div pi 2 div,
    linecolor={[cmyk]{1,0,1,0.5}},linewidth=0.75\pslinewidth,
    ngrid=50,
    %RotY=90,
    RotX=-90,
    function=klein]%
}
\end{pspicture}
 
\end{document}