 So now we've nearly completed our creation of our thesis in polygons. We're going to look at step four, which is creating what's called a Voronoi diagram, which is essentially finishing the thesis in polygons. So here I have now identified the ortho centers for each of the 12 triangles, each of my 12 Delaunay triangles. And you can see 11 of the ortho centers are here on the page, and one of the ortho centers is off the page here. Now what I'm going to do is I'm going to go ahead and divide this area, this space, into polygons, into regions. And if you remember, one of the properties of our bisectors here are these bisection points, is that it split the distance between, may the distance that it was equal in between two points, like the 4.66 here, and the 6.01, which means all the territory that's in this area, all the area that's near this 4.66 on this side of this bisector, is closer to the 4.66 than it is to the 6.01. Well, I'm going to go ahead and connect ortho centers. In this case, I'm going to connect ortho centers along this line through that particular point there. And I'm establishing the territory that belongs to the 4.66. For this particular point here, I can see there's a dividing line between the 3.86 and the 4.66. There's nothing to connect to here, but I do know that there's that bisecting line that's going to go ahead and extend off the page. Similarly, over here, the dividing line between the 4.66 and the 5.37 is this line here. But I'm going to take the extension of that line and extend it off the page. And now I've created the territory for 4.66, or the beginning of a thesis in polygon. Notice if I consider that same idea, I'm going to continue to draw around and let's claim the territory that's associated with this 6.01 value. And we do that simply by connecting the ortho centers through the extensions of those bisectors. I see the same thing if I follow these connections. I now have established territory associated with this value of 5.06, a polygon associated with 4.39. If I connect the invisible ortho center here by extending those lines, I've created polygons for 5.37 and 4.67. Similarly, extending lines for each of those. And if I see here there's a perpendicular bisector that I haven't extended, I will go and extend that out there. And now I have divided my region into a series of thesis in polygons. Each of these polygons is what we consider to be a thesis in polygon. The entire process is called a Voronoi diagram.