Magnetic Klein Quartic
A physical model of the Klein quartic, a genus-3 hyperbolic surface tiled by 24 regular heptagonsmbuilt from neodymium magnets.
The Klein quartic is an algebraic curve of genus 3 — topologically a surface with three holes — whose 168-element symmetry group is the largest possible for any genus-3 surface. It can be realised as 24 regular heptagons meeting three at every vertex, tiling a hyperbolic surface.
Spherical neodymium magnets bond naturally at 120° angles, which is exactly the interior angle needed for three heptagons to meet.
The assembly proceeds in “pants”: each pair of pants is a surface with three boundary circles, made of six heptagons. Four pants glued at their openings produce the complete Klein quartic. The model buckles into a saddle-like form under its own hyperbolic curvature, accurately representing the negative Gaussian curvature of the abstract surface.