Throughout the series, three recurring integers, being One, Two and Four, have shown a pocket realm connected to them, often being used to store eliminated players.
One's Dimension (One)[]
- Main article: One's Dimension

One's Dimension has three seen sections:
- An ominous room resembling a library, which One uses to make deals with the contestants, and imprison those who refuse her deals in One's field. The room has a table that has the unique ability to effect the real world, used to spread a continental storm in "Category One".
- A field in the same color as One, with yellow flowers and a path leading to a doorway into the Equation Playground.
- The Vortex: a debatable area used by one as a gateway to transport herself and contestants between the real world and her own. Interestingly, this makes One's pocket world the only one to which the main entrance isn't the corresponding algebralien's appendage or body.
Inhabitants[]
Former[]
Elimination Space (Two)[]
- Main article: TPOT elimination space

The Elimination Space is Two's area used to store eliminated players in The Power of Two. The region is upside down, resembling a Japanese cityscape, however a barrier blocks of any buildings outside a singular modern hotel. Whether Two made this barrier or not is currently unknown, as One is shown to be able to influence this area.
Inhabitants[]
Former[]
The Fourest (Four)[]
- Main article: The Fourest

The Fourest is a dark blue forest landscape used by Four to contain the eliminated contestants of Battle For BFDI and others he has a distaste towards. The area has many worldbending structures and Four themed regions, alongside several portals to other dimensions. One is shown to be able to enter this region.
Inhabitants[]
Former[]
Rejoined[]
Evicted[]
Escaped[]
Minor[]
X's Dimension (X)[]

A glimpse of what could be X's Dimension can be seen in "Seasonal Shift". The only information known about it is that the place is potentially yellow. Unlike the other dimensions, this one has only been shown in an alternate timeline, so whether or not it exists in the main one is up for debate.
Inhabitants[]
Two Thousand, Seven Hundred, Sixty-Three's dimension[]

Due to Two Thousand, Seven Hundred, Sixty-Three's capability of transport across dimensions, it is possible they have one of their own, which they may use to hold their victims. However, nothing about this dimension is known, except for its possible existence.