f[x_, y_, z_] := y^2 - x^2 - 2 + z*(x^2 + y^2 - 4)
 object =
 ContourPlot3D[f[x, y, z] == 0, {x, -5, 5}, {y, -5, 5}, {z, -5, 5},
  Mesh -> False, PlotPoints -> 20, Extrusion -> 0.5]
Export["~/print.stl", object]