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00011011more colours
  allowing for all combinations of revolution ('time') and rotation ('spin') we would have eight distinguishable versions,
but four of them at first have no obvious geometric equivalent as projection of an 'unrolling line' (cycloid, trajectory),
to construct them we have to invert the motion of shadows on the ribbons, as it can be viewed on the 4:1 link below.

 
   explanation of terms
 ©  Wolfgang W. Daeumler

 

 
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4:1, all eight versions