Torus Knots

A closed curve winds around a torus in two directions. Parallel strands make a sculptural ribbon; small breaks at crossings reveal which strands pass in front.

Torus Knots: A closed curve winds around a torus in two directions. Parallel strands make a sculptural ribbon; small breaks at crossings reveal which strands pass in front.Torus Knots: A closed curve winds around a torus in two directions. Parallel strands make a sculptural ribbon; small breaks at crossings reveal which strands pass in front.

About this shape

Torus-knot geometry · coprime winding numbers

Torus Knots, knot theory, drawn by GART: A closed curve winds around a torus in two directions. Parallel strands make a sculptural ribbon; small breaks at crossings reveal which strands pass in front.
Torus Knots · CC BY 4.0

The two winding numbers are coprime, so each strand forms one closed knot rather than a disconnected link. Nearby minor radii make a ribbon on the torus. Short projected spans are sorted by depth and drawn with a paper-coloured clearance before the ink, opening the crossings.