Trefoil

A gallery of torus knots

TrefoilKnots as sculpture.

Stoneware forms of T(p,q) in oxblood glaze, thrown on a slow wheel under cold studio light. The placard tells you what the eye can't: how many crossings each piece can never lose. Tap the piece — it will not give.

The collection

Four vessels, one rule.

Every piece here is wound on the same lathe: p strands carried q times around a torus, then fired. Choose a vessel and the wheel re-throws the clay in front of you.

Invariance

Can it untie?

House rule: you may bend the clay, stretch it, slide it along itself — but never cut it, never pass it through itself. Under that rule, every number on the placard is permanent.

The trefoil's three crossings cannot be wiggled down to zero — Fox's three-colouring proves it is not an unknot in disguise. Crossing number, genus, the catalogue mark: none of them survive by shape. They survive by law.

A knot doesn't hold its form. It holds its numbers.

Conservator's test

  1. Grip the piece anywhere along the strand.
  2. Pull, twist and slide — as hard as you like.
  3. Count the crossings again.