Moveable Bar Chords on the 6th string

Bar chords are often torturous for beginning guitarists, but they unlock the neck of the guitar like no other chords can do.
With the 3 chord shapes in this post and knowledge of the 6th string (to the 12th fret), you now have 36 chords at your disposal (theoretically more if you count enharmonic equivalents as different chords-but let's not worry about that too much).

First, let's look at the 3 shapes in question:

Major:

minor:

7th:

These shapes are based around the open position E chord. If you take away the first finger bar, you probably can see the the E, Em and E7 shape.

These chords change letter name based on where you place that first finger bar. When you know the notes on the 6th string, you really have some options.

These are the first steps in mapping the neck of the guitar. Happy chord hunting!