Trefoil Knot — 3D

The trefoil is the simplest non-trivial knot (3₁): three crossings, cannot be untangled without cutting. Parameterized as (sin t + 2sin 2t, cos t − 2cos 2t, −sin 3t). Drag to rotate. Knot invariants distinguish it from the unknot.

Tube radius7
Resolution120
Rotation4
Crossing number3
Writhe (blackboard framing)±3
Alexander polynomialt⁻¹ − 1 + t
Jones polynomial−t⁻⁴ + t⁻³ + t⁻¹
Seifert genus1