Lissajous Space Curve

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  lissajous2_3_7 curves
lissajous curves 001
Lissajous 2 3 7 knot. It represents an alternating knot, because along the curve overpasses and underpasses alternate. Alternating knots cannot be drawn with fewer crossings. The knots with seven crossings are classified and this one is denoted 7_4.
lissajous4 3 23 knot 001
lissajous 4 3 23 knot
There are two views in this sequence where overpasses and underpasses alternate. This lissajous space curve is an alternating knot, hence cannot be drawn with fewer crossings.
lissajous2 5 13 knot 001
lissajous 2 5 13 knot
There are two views in this sequence where overpasses and underpasses alternate. This lissajous space curve is an alternating knot, hence cannot be drawn with fewer crossings.

Lissajous_Curves__prime_knot_7_4.pdf