All torus knots with one strand or for which the number of parallel strands times the number of times they wind around the meridian is equal to -1, 0, or +1 are trivial: they can be continuously deformed into a standard torus without committing self-intersections in the process. All other torus knots are non-trivial.


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See notes on .stl files





(1, 5, -10/5)

.stl file


(1, 5, 0)

.stl file


(1, 5, 10/5)

.stl file



(3, -1/3, -5/5)

.stl file


(3, -1/3, 0)

.stl file


(3, -1/3, 5/5)

.stl file


(3, 2/3, -5/5)

.stl file


(3, 2/3, 0)

.stl file

(3, 2/3, 5/5)

.stl file




(4, 2/4, -5/5)

.stl file


(4, 2/4, 0)

.stl file


(4, 2/4, 5/5)

.stl file



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