# Drawing the Möbius band and the Klein bottle

I have this:

\begin{tikzpicture}
\begin{axis}[hide axis, unit vector ratio=1 1 1, view={-30}{45}]
\addplot3 [surf, domain=0:360, y domain=-1:1] (    {(10+y*cos(3*x/2)))*cos(x)}, {(10+y*cos(3*x/2)))*sin(x)}, {y*sin(3*x/2)});
\end{axis}
\end{tikzpicture}


But it doesn´t works. I don´t know the reason. I would like to obtain exactly one of these:

Additionally, I´d like to draw a simple Klein bottle (without grid or shadows), but in this case I´ve nothing... :(

Thanks for the support!!

A colored Moebius band (run with xelatex):

\documentclass[pstricks]{standalone}
\usepackage{pst-3dplot}

\makeatletter
\define@key[psset]{pst-3dplot}{HueBegin}{% Between 0 and 1
\def\PstHSB@HueBegin{#1}}
\define@key[psset]{pst-3dplot}{HueEnd}{% Between 0 and 1
\def\PstHSB@HueEnd{#1}}
\define@boolkey[psset]{pst-3dplot}[Pst@]{HSB}[true]{}
% Default values
\psset[pst-3dplot]{HueBegin=0,HueEnd=1,HSB=false}
\psset{dimen=outer}

\def\parametricPlotThreeD@iii{%   without arrows (quickplot)
\psk@ThreeDplot@yPlotpoints {
/Counter 0 def
/t tMin def
xyz \@nameuse{beginqp@\psplotstyle}
\psk@ThreeDplot@xPlotpoints\space 1 sub {
xyz
1 Counter eq { moveto currentpoint /OldY ED /OldX ED }
{\ifPst@HSB % Other points than the first one
/PointY exch def
/PointX exch def
Counter \psk@ThreeDplot@xPlotpoints\space div
\PstHSB@HueEnd\space
\PstHSB@HueBegin\space sub mul
1 1 sethsbcolor
OldX OldY PointX PointY lineto lineto
stroke
PointX PointY moveto
/OldX PointX def /OldY PointY def
\else lineto \fi } ifelse
} repeat
/t t dt sub def
} repeat
}%
\@nameuse{endqp@\psplotstyle}%
}
\makeatother

\begin{document}
\psset{Beta=20}
\begin{pspicture}(-6,-3)(6,3)
\parametricplotThreeD[plotstyle=line,xPlotpoints=100,
yPlotpoints=100,drawStyle=xyLines,HSB](0,365)(-1,1){
t 2 div sin u mul }
%\pstThreeDCoor[xMin=-1,yMin=-1,zMin=-1]
\parametricplotThreeD[plotstyle=line,xPlotpoints=100,yPlotpoints=1,
linecolor=black,linewidth=1.5pt](488,-60){
t 2 div sin }
\parametricplotThreeD[plotstyle=line,xPlotpoints=100,yPlotpoints=1,
linecolor=black,linewidth=1.5pt](631,513){
t 2 div sin }
\end{pspicture}
\end{document}


\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\begin{document}
\begin{tikzpicture}[declare function={moeb=3;phase=120;}]
\begin{axis}[hide axis, unit vector ratio=1 1 1, view={-30}{45}]
{(10+y*cos(moeb*x/2+phase)))*cos(x)}, {(10+y*cos(moeb*x/2+phase)))*sin(x)}, {y*sin(moeb*x/2+phase)});
\end{axis}
\end{tikzpicture}
\end{document}


You may change the plot by playing with moeb, phase and point meta.

I am not trying to give an exact answer but point out that your comment that gridded and grey is not desirable so taking your code example as found on this site with a few adjustments putting back we get this which I guess is a reasonable rendering That does help many people to understand the nature of a mobeius

But if you try to remove the grid and the color as you have done you will at best get a dot.

Equally there are many answers for bottles on this site that you can adapt by removing the features you don't want, but removing the grids make them less understandable.

Thus you could remove the lables from this one https://tex.stackexchange.com/a/77643/170109

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