What is the relationship of 'added edges' to existing 'faces/edges'?

example:
I made a block with 10 divisions on the X-axis and 10 on the Y-axis.
Then I wanted to Cut Out a diamond shape from one of the divisions so first I tried by adding the edges of the diamond, then 'filled holes' between the new edges.
BUT when I tried to then Cut the diamond shape out I found all I could do was cut either the whole 'square' or just the 'faces' surrounding the diamond leaving the diamond that I wanted removed.

OK, I finally figured out I was working in the 'wrong direction' (from inside to outside) and finally just deleted the whole 'square' division and then added Edges to form my diamond and then 'fill holes' to add back the outter faces. Done deal, I got what I wanted....

But now I am not sure just what is the relationship of "add edge" to the existing mesh if the added edges to not actually divide the face they are formed across??
(hope this makes sense?)

Attached Link: http://www.sciformz.com

Wow, I think I am confused. WOuld love to see some screen captures of what you did. Why not draw a profile and sweep around a line to get your diamond?

On the left is the final result I got by removing the 4 divisions where I wanted the diamond cut-out. I then drew in the new edges and filled the holes.

The left is a demo of my first (failed) method of trying to "add" the edges/fills and then "cut" the diamond out.

My question is:
On the Left image, what is the relationship of the Added Edges (in green) to the 'original' faces?
I had thought that the 'new edges' would have 'divided' the faces, but they appearently do not??

I'm trying to better understand the Point/Edge/Face relationship to get a better grasp on how to proceed when begining a project from scratch.

(also let me point out that I have no 'training' in modeling and just trying to 'blaze my own path' in my "spare time" ;-P

Attached Link: http://www.sciformz.com

Well, ok, I am not the expert on mesh control. But what I can say is this: Simply adding a face or even a segment to an existing shape does not necessarily mean you are altering the construction of the shape UNLESS that program constitutes it. The "added edges" are simply another object I believe. They are not one in the same. For example, in my program, there is a tool to "Add segment" to an existing object. That then becomes part of that object respectively. The key thing to remember is that there are many ways of doing things in a modeling program to achieve the same results. Find a method that is easiest for you to accomplish what you want or one that you feel comfortable with. Gees, I hope I explained myself well enough. Sorry if I confused you more. :)