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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