Klein Bottle

klein bottle 50997
klein bottle
aa = 3;
ParametricPlot3D[
 {(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, 2 Pi},
 Boxed -> False, Axes -> False, BoundaryStyle -> {Thin, Black}]