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Spheres & Flow · 3D

Torus Knot

(p, q) winding

Torus Knot, drawn as a glowing line figure

A single closed thread wound around a torus: p times around the axis, q times through the hole. If p and q share no factor it is a true knot.

Knot if
gcd(p,q) = 1

Open in SacredForm

Turn it in your hands, strike it to hear the chord of its edges, slice it with a plane.

Facts

  • The (2, 3) torus knot is the trefoil, the simplest knot.
  • Seen from above it becomes a rose-like star.
  • (p, q) and (q, p) are the same knot.

Related figures