The Box

Dimension Box-1
Dimension Box-1 is the Original Box dimension, it's an empty, featureless box.

Dimension Box-2
Dimension Box-2 is the Box dimension after Darth converted it. The Thunderhoof Empire was created here. It was eventually abandoned in favor of Dimension Box-3

Dimension Box-3
Dimension Box-3 is the last Box-x Dimension to have empires. It fell due to superweapons being used, and it's inhabitants fled to the Valley.

Current Box Dimension
The old Box dimension has since it's abandonment been replaced. All old land has been built over by Aperture Science, and it is now filled with combat chambers built to train Robot Soldiers and such. It is governed by GLaDOS, who cares little about the lives of others, and won't hesitate to kill off intruders using a Deadly Neurotoxin.