Klein quartic tiled by heptagons

cults3d

A Model of the Klein Quartic: A Complex Figure Revealed This captivating object exhibits three distinct properties simultaneously: a hyperbolic surface composed of 24 regular heptagons that intersect at every vertex in groups of three; the surface defined by the equation x³ y + y³ z + z³ x = 1, boasting the largest possible symmetry group among surfaces of genus-3 (this is the simple group with a total of 168 members); a modular curve known as X(7), which results from dividing the Poincaré half-plane by matrices congruent to 1 modulo 7; each point on this curve corresponds to an elliptic curve featuring 7-torsion. In this model, each heptagon is assigned a fraction based on the Stern-Brocot tree, with values reduced modulo 7.