Wiman's sextic explained

In mathematics, Wiman's sextic is a degree 6 plane curve with four nodes studied by .It is given by the equation (in homogeneous coordinates)

x ^{6+y} ^{6+z} ^{6} + (x ^{2+y} ^{2+z} ^{2)(x} ^{4+y} ^{4+z} ^{4)=12} x ^{2y} ^{2z} ^{2} Its normalization is a genus 6 curve with automorphism group isomorphic to the symmetric group S₅