Hopf Link

Twelve circles, every pair linked once

Every point of a sphere has its own circle in four-dimensional space, and any two of those circles are linked. Projected into our space, the circles over one line of latitude lie on a single torus, winding around each other. We took twelve of them and cast them.

(z₁, z₂) ↦ (2 z₁ z̄₂, |z₁|² − |z₂|²)S¹ → S³ → S²

Finish

€59.00

No VAT charged under §19 UStG. Plus shipping.

Size
24 × 25 mm, 18 mm deep
Weight
≈ 5.7 g
Material
316L stainless steel, PVD

Twelve fibres of the Hopf fibration, stereographically projected from the 3-sphere: round circles on one torus, each linked once with every other. In the maths they never touch; in steel the wires meet where they pass closest, so the piece is cast as one.

Hopf Link

Worn and boxed

Hopf Link Hopf Link Hopf Link

The photos are AI-generated visualisations of the real design.