I figured you wanted to animate it with the taking it apart bit in there. Sigh, there goes my shortcut and lazy exit haha. Technically you could split edges, cut, extract faces, merge vertecis, and append to polygons, but the process is not very beginner friendly. It's not hard but maybe not for the first steps to take. It's fast and lovely later on though when you are more comfortable with those techniques.

For now:
You can proceed with what you have too no worries. If you want you can clean up edges that aren't needed to alter the form. The cube example again. If you have a cube it does not need 20 edges to describe that, right. So delete all unecessary edges. This is time consuming too :p and remember the object should still maintain all quads (four sided faces) so delete all the way around.
I am also saying you don't have to do this. With all of the above I just want to illustrate how you could of done different and more efficient for the next project or how to save this one if it would be 1 million polygons and up. Then you'd be in REAL trouble :p

Now, when you delete edges rather than pressing delete I recommend adding Edit Polygons->Delete edge on to the shelf and use that (hold ctrl+shift as you select the menuitem)
Using delete edge deletes the unwanted vertices too. If you just press delete, the edge will disappear, but not the vertices where it used to connect stays.