Take a look at this: This is a triangulation of a set of random points, such that all the points are connected to one another, all of the faces are triangles, and the edges include the convex hull of the points. I would like to claim that this is not a very “good” triangulation. This algorithm tends to produce lots of long, slivery triangles, and a really uneven distribution of edge counts across different vertices – some vertices have way more edges than they need to. Here’s a different triangulation. These are the exact same points, but I triangulated them smarter: