 Klein quartic

The Klein quartic has the smooth projective plane modelIts affine chart $Z=1$ is $x^{3}y+y^3+x=0$. If $\zeta$ is a primitive seventh root of unity, the projective transformationis an automorphism of order seven.

The Klein quartic is a notable and interesting example of a mathematical object in the field of topology and algebraic geometry. Specifically, it is a compact Riemann surface of genus 3, which can be represented as a complex algebraic curve of degree 4.