The Klein quartic x³y + y³z + z³x = 0, named after Felix Klein, is a Riemann surface, and a curve of genus 3 over the complex numbers C.

The Klein quartic has automorphism group isomorphic to the projective special linear group G = PSL(2,7). The order 168 of G is the maximum allowed for this genus 3; and this curve is uniquely determined by requiring that the symmetry is as large as this.

Klein's quartic occurs all over mathematics, in contexts including representation theory, homology theory, octonion multiplication, Fermat's Last Theorem, and Stark's theorem on imaginary quadratic number fields of class number 1.

External links

• Polyhedral models of Felix Klein's quartic (http://www.math.uni-siegen.de/wills/klein/)
• The Eightfold Way: The Beauty of Klein's Quartic Curve (http://www.msri.org/publications/books/Book35/contents.html)