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Is this transform actually possible? Which is gluing edges of two Mobius bands to make a torus? I tried to do it physically with pieces of paper, but I couldn't complete it. The detailed explanation and image reference is in here, at figure 19.

  • $\begingroup$ have you seen (math.stackexchange.com/q/1036755) ? $\endgroup$
    – Jean Marie
    Aug 14, 2016 at 6:50
  • $\begingroup$ @JeanMarie I've seen it now, but still I'm confused. Are you implying that it is impossible to achieve the upper process with a piece of paper? $\endgroup$
    – 7_G.S.N
    Aug 14, 2016 at 9:23
  • 4
    $\begingroup$ The torus is orientable, so cannot contain a non-orientable submanifold of the same dimension. In particular, the torus cannot contain a Mobius band. $\endgroup$
    – user98602
    Aug 14, 2016 at 15:59


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