What do you do to determine what the pivot note a mirror inversion should be?

Example: Key of C; Mode: Lydian; B is 3 half steps above G# (pivot), 3 half steps more is F which begins the Lydian scale of C. All modes should rotate (and I believe they do) around D or G#; Thus:

Aeolian/Myxolydian | Lochrian/Lydian | Ionian/Phrygian | Dorian/Dorian(I think) in every key...

So for a mirror inversion I believe its 3 half steps up and the normal is 3 half steps down (I hope I'm write, dont want to sound like a fool ^_^)