Lissajous knots and billiard knots

Volume 42 / 1998

Vaughan Jones, Józef Przytycki Banach Center Publications 42 (1998), 145-163 DOI: 10.4064/-42-1-145-163


We show that Lissajous knots are equivalent to billiard knots in a cube. We consider also knots in general 3-dimensional billiard tables. We analyse symmetry of knots in billiard tables and show in particular that the Alexander polynomial of a Lissajous knot is a square modulo 2.


  • Vaughan Jones
  • Józef Przytycki

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