"Klein's quartic curve is a surface of genus 3 (a three-holed torus) of constant negative curvature. It can be constructed by specifying a 14-gon in the hyperbolic plane and identifying pairs of edges. However, it can also be constructed as the solution to Klein's wonderfully simple equation:
u3v + v3w + w3u = 0
You can read Klein's derivation of this equation in his original article on the quartic curve, “On the Order-Seven Transformation of Elliptic Functions”, translated into English in this book:
The Eightfold Way: the Beauty of Klein's Quartic Curve, edited by Silvio Levy; MSRI Research Publications 35, Cambridge University Press, Cambridge 1999."
5 out of 5
http://www.gregegan.net/SCIENCE/KleinQuartic/KleinQuarticEq.html
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