Bring's curve

In mathematics, Bring's curve (also called Bring's surface) is the curve given by the equations

It was named by Klein (2003, p.157) after Erland Samuel Bring who studied a similar construction in 1786 in a Promotionschrift submitted to the University of Lund.

The automorphism group of the curve is the symmetric group S₅ of order 120, given by permutations of the 5 coordinates. This is the largest possible automorphism group of a genus 4 complex curve.

The curve can be realized as a triple cover of the sphere branched in 12 points, and is the Riemann surface associated to the small stellated dodecahedron. It has genus 4.