Complex 2D Models
(Face combinations on an octagon)

The vertex points are marked on the wireframe diagram to show that they have not changed.  They are the same vertex points and are in the same spots for each sample.  The difference between each example is the face definitions, not the verticies.
 

Three faces - four points each
1st face uses vertex points 1,2,3,0
2nd face uses vertex points 0,3,4,7
3rd face uses vertex points 7,4,5,6

 
Three faces - four points each
1st face uses vertex points 0,1,2,7
2nd face uses vertex points 7,2,3,6
3rd face uses vertex points 6,3,4,5

 
Three faces - four points each
1st face uses vertex points 2,3,4,1
2nd face uses vertex points 1,4,5,0
3rd face uses vertex points 0,5,6,7

 
Six faces - three points each
1st face uses vertex points 1,2,0
2nd face uses vertex points 2,3,0
3rd face uses vertex points 0,3,7
4th face uses vertex points 3,4,7
5th face uses vertex points 7,4,6
6th face uses vertex points 4,5,6
Note : when defining triangle faces, be sure to leave the last value set to negative one (-1)

By no means does this exhaust all possible combinations of face definitions.  You could vary the three point versions as many times as I have shown with the four point versions.  You could combine the three point and four point versions in many ways as well.

My aim here is to demonstrate that faces may be created in almost any way you can think up.  On basic models, this may not seem like a big deal, but as your models grow in complexity, you will come to appreciate this freedom in design.