Here is a parametric formula for the Klein bottle.
aa=3;s=1;
ParametricPlot3D[
s*{(aa+Cos[v/2]*Sin[u]-Sin[v/2]*Sin[2*u])*Cos[v],
(aa+Cos[v/2]*Sin[u]-Sin[v/2]*Sin[2*u])*Sin[v],
Sin[v/2]*Sin[u]+Cos[v/2]*Sin[2*u]},
{u,0,2*Pi},{v,0,6}]
The aa constant controls the overall radius of the torus shape. If aa is large, the object will be like a thin tube. The s is the scaling factor for the whole thing. u is the sweep of the figure-8 profile. 0 to 2 π. v is the sweep of the torus tube. 0 to 2 π.