2020-20 Efficient triangulation of surfaces

Let \(S_g\) denote the closed orientable connected surface of genus \(g\). Suppose we glue triangles along the edges so that the resulting space is \(S_g\) and the intersection of any two triangles are either empty or a single edge. Let \( n(g) \) be the minimum number of triangles one needs to make \(S_g\) while satisfying the above rule. What are \( n(1), n(2), n(3) \)? Does the limit \( \lim_{g \to \infty} n(g)/g \) exist?

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