Pensieve Header: The Klein bottle based on http://en.wikipedia.org/wiki/File:Klein_bottle.svg.

p[u_,v_] := Which[
v<Pi, (* the lower rim *)
  {(2.5-1.5*Cos[v])*Cos[u], (2.5-1.5*Cos[v])*Sin[u], -2.5*Sin[v]},
v<2*Pi, (* the "body" *)
  {(2.5-1.5*Cos[v])*Cos[u], (2.5-1.5*Cos[v])*Sin[u], 3*v-3*Pi},
v<3*Pi, (* the upper bend *)
  {-2+(2+Cos[u])*Cos[v], Sin[u], (2+Cos[u])*Sin[v]+3*Pi},
True, (* the back feed from the upper ned to the "inside" *)
  {-2+2*Cos[v]-Cos[u], Sin[u], -3*v+12*Pi}
];
ParametricPlot3D[
p[u,v],
{u, 0, 2Pi}, {v, 0, 4Pi}
]