I’m trying to make a shirt. My mesh started with a cube where I divided each face into 9 faces using Loop Cut (ctrl-R). I then moved my vertices around, used Set Smooth on the mesh, set my material to a certain color, and then attempted to add a stencil (or a tga image with alpha transparency). Adding a camera and one lamp behind it, I got this

Yeah, it’s a shirt with a wrinkle, but I had NO intention of adding any wrinkles. As you can see, the ‘88’ is placed everywhere there is a face. Looking at the Solid version, I noticed little diagonal lines dividing my quads, especially on the lower faces. These appear more obvious in Set Smooth than Set Solid.

So I’d like to ask, what on Earth are these lines doing in my quads?

As a simpler example above, I took a cube mesh and moved the top left foreground corner to the right and a bit into the cube (along the y-axis). Here you can see two of the diagonals, one making the darker shaded area and the other making a triangle on the top of the cube. Now why isn’t there a diagonal connecting the bottom left foreground vertex with the top left background vertex? Was I just fortunate to move the vertex that was on one end of this face’s diagonal? Is this normal to you all in modeling? Why does this occur?

I’ve noticed these little triangles for sometime in my other meshes, much to my annoyance, and my only recourse was to delete the offending vertices, replace them with extruded copies from a neighboring vertices, and remake the faces with the F button. And forgive me if this problem has already been posted, but it’s nearly impossible for me to figure out a better string of keywords that relate to it.