Each band is generated by a line segment that moves with the Frenet frame and rotates within the normal-binormal plane of that frame. Since the frame returns to its original position, the band is orientable if the number of rotations is integer and it is non-orientable if twice that number is odd.


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See notes on .stl files






(1, 5, 0)

.stl file


(1, 5, 10/2)

.stl file


(1, 5, 20/2)

.stl file


(3, 4/3, 0)

.stl file


(3, 5/3, 0)

.stl file


(3, 6/3, 0)

.stl file


(3, 2/3, -2/2)

.stl file


(3, 2/3, 0)

.stl file


(3, 2/3, 2/2)

.stl file



(3, 1/3, 0)

.stl file


(4, 1/4, 0)

.stl file


(5, 1/5, 0)

.stl file


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