# 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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