# Triangulation of surfaces and the number of edges in a triangulation.

I am reading a chapter on surfaces and triangulations, but I think I am losing the plot.

I can't see why (1) is not $V(\Gamma) = c$ and (2) $E_0(\Gamma)= h+c$.

I would be grateful if someone could clear things up!

From what I understood, the holes will contract into vertices after the triangulation. Therefore, when trying to count every vertex, we sum the vertices from the ciliated boundaries and the new vertices that before were holes.

• Ahh. Okay, thanks! – harry dunlop Mar 4 '14 at 17:26