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Remember that all polygonal geometry is made up of triangles, and the reason we see quads is because the triangles are hidden by default in order to make working with the model easier and less jumbled. As I mentioned briefly in Chapter 2, sometimes it is advantageous to model with your triangle edges visible as opposed to the default quad façade. Edge placement is often crucial in determining the shape of a polygonal object.
As your models become more complex and your poly counts increase, you’ll find it more and more difficult to keep your mesh clean and stable. In certain cases, looking closely at the internal structure of triangles in your model will help you ensure that it is as clean as can be.
Another advantage to working with triangle edges is that you have the option to turn or flip tri edges. There are several reasons why this is beneficial. As an example, the placement or orientation of an edge on a polygonal face could determine the placement of the bridge of a nose or the placement of the cheeks. Take a look at the default sphere shown in Figure 6.28 with triangle edges visible; you can see that they are all facing the same direction. By flipping certain tri edges, you can actually manipulate the geometry in ways that were not possible with the previous version of the sphere.