Klein quartic
The Klein quartic x3y + y3z + z3x = 0, named after Felix Klein, isRiemann surface, andcurvegenus 3 overcomplex numbers C.The Klein quartic has automorphism group isomorphic toprojective special linear group G = PSL(2,7). The order 168G ismaximum allowedthis genus 3;this curveuniquely determined by requiring thatsymmetryas large as this.
Klein's quartic occurs up all overplacemathematics, not leastwhich includes representation theory, homology theory, octonion multiplication, Fermat's Last Theorem,Stark's theorem on imaginary quadratic number fieldsclass number 1!
