I printed the graph as follows, but part of it is cut off.
KleinBottle[a_, b_] := Module[{bx, by, rad, X, Y, Z, u, v},
bx = 6 Cos[u] (1 + Sin[u]); by = 16 Sin[u];
rad = 4 (1 - Cos[u]/2);
X = If[Pi < u <= 2 Pi, bx + rad Cos[v + Pi], bx + rad Cos[u] Cos[v]];
Y = If[Pi < u <= 2 Pi, by, by + rad Sin[u] Cos[v]];
Z = rad Sin[v];
ParametricPlot3D[{X, Y, Z}, {u, 0, a}, {v, 0, b},
PlotStyle -> {FaceForm[Red, Red], Opacity[0.5]},
Axes -> None, Boxed -> False, PlotPoints -> 30, ImageSize -> 600, Mesh -> None]];
KleinBottle[2 Pi, 2 Pi]
Why is the graph truncated?
Exclusions -> None
, and report back. See this older question as well. $\endgroup$