Although the abbreviation doesn't make sense to me I've read that ADX stands for "Administrative Maximum Facility".
But if so it should say AMF instead of ADX. ADX might stand for something else but I can't find anymore information on it.
I do know though that the ADX Supermax prison is known to be a horrible prison with really secure facilities and tight restrictions and inmates are in their prison cells for 23 hours per day except to come out to a little recreation cage for 1 hour and then they get put back in their prison cell for another 23 hours.
They don't get out of their prison cell everyday either so sometimes the prisoners are in their prison cells for 24 hours per day and all they have is a tiny little window to give them a little sunlight and not much more.
There showers are also located in the cells and when they do come out of their cells they're in leg irons, and waist chains etc and escorted by a few guards to the rec cage and back to their prison cells.