Prime Knots

Modify the curve

tube thickness, 1 ... 16:


soul radius, 4 ... 6:


meridian frequency, 1 ... 9:


twist parameter, 0 ... 4.2:


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To obtain these curves first look at torus knots with frequencies (2,3), (2,5) and (2,7).
Then twist one of the leafs to obtain more alternating crossings, implying that the obtained curves are nontrivial knots.
Such alternating knots cannot be drawn with fewer crossings.

Morph_Prime_Knots_5_4_3.pdf