Smoother curves in a tikz

Question

I made the following picture using ipe. The picture corresponds to the Moebius tape, well, something related. Anyway, how can I do a better picture with smoother curves? Maybe Tikz, I don't know.

Answer 1

I guess the question is more how to parametrize it. Here is one suggestion.

\documentclass[tikz,border=5pt]{standalone}
\usepackage{tikz-3dplot}
\begin{document}
\tdplotsetmaincoords{50}{180}
\begin{tikzpicture}[tdplot_main_coords,scale=2]
% \draw[-latex] (0,0,0) -- (2,0,0) node[below]{$x$};
% \draw[-latex] (0,0,0) -- (0,2,0) node[below]{$y$};
\draw[-] (1,0,-3) -- (1,0,2);
\draw plot[domain=0:{2*pi},samples=100,variable=\x] 
({cos(\x*180/pi)*(1+0.2*cos(\x*180/pi))/1.2},{-sin(\x*180/pi))},{-cos(90*\x/pi)})
-- plot[domain=0:{2*pi},samples=100,variable=\x] 
({cos(\x*180/pi)},{-sin(\x*180/pi))},{cos(90*\x/pi)});
\draw plot[domain=0:{2*pi},samples=100,variable=\x]
({cos(\x*180/pi)},{-sin(\x*180/pi))},{-2.4+0.4*cos(180*\x/pi)});
\node[circle,fill=black,draw,label=above left:$0_2$] at (1,0,1){};
\node[circle,fill=black,draw,label=above left:$1_2$] at (1,0,-1){};
\node[circle,fill=black,draw,label=above left:base] at (1,0,-2){};
\end{tikzpicture}
\end{document}

You can play with the parametrization and view angles in order to adjust it.