# Translation surfaces

I know that this definitely have some sort of reference out there, but I did not find any wikipidea page for it or any introductory Mathematical article about it . I just want definition and concrete examples of translation surfaces. For example, if I take four copies of equilateral triangle and glue them together side by side to form a tetrahedron, how do I put a Riemann surface structure on it ? I want some detailed explanations etc. Could you cite any reference(s) ?

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There is a huge literature, and I'm not sure exactly what you are looking for. That being said, Masur-Tabachnikov's survey "Rational billiards and flat structures" and Masur's survey "Ergodic Theory of Translation surfaces" contain a lot of introductory material. Both can be found on Masur's webpage here.

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Check this thread, it is amusing and you are involved:  tea.mathoverflow.net/discussion/802/a-reputation-table-bug  –  Will Jagy Dec 1 '10 at 19:49