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Klein quartic tiled by heptagons

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3D model description

A model of the Klein quartic. This fascinating object is at the same time:

  • a hyperbolic surface tiled by 24 regular heptagons, with three of them meeting at every vertex (or dually: by 56 equilateral triangles, seven of them around each vertex);

  • the surface with equation x³ y + y³ z + z³ x = 1, which has the largest possible automorphism group for a genus-3 surface (this is the simple group with order 168);

  • the modular curve X(7), which is the quotient of the Poincaré half-plane by the group of matrices ≡ 1 (mod 7); each point of this curve defines an elliptic curve with marked 7-torsion.

In this model, each heptagon is labeled by a fraction, according to the Stern-Brocot tree (modulo 7).

  • 3D file format: STL and SVG
  • Publication date: 2020/02/05 at 08:17





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