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The Double Cover of an Annulus

JavaView applet, left click and drag to rotate, right click for help and further options.

 

 

Mathematica code:

ParametricPlot3D[
  {
    {r Cos[2t], r Sin[2t], 4 + Cos[t]},
    {r Cos[t], r Sin[t], 0},
    PlotPoints -> {49, 2}
  },
  {t, 0, 2Pi}, {r, 1, 3}
]