  We show that every open Riemann surface can be obtained by glueing together a
countable collection of equilateral triangles, in such a way that every vertex
belongs to finitely many triangles. Equivalently, it is a _Belyi surface_:
There exists a holomorphic branched covering to the Riemann sphere that is
branched only over three values. It follows that every Riemann surface is a
branched cover of the sphere, branched only over finitely many points.
