Cube square inscribing is the problem of finding the area of the largest square that can be inscribed on a unit cube (Trott 2004, p. 104). The answer is 9/8, given by a square with vertices (1/4, 0, 0), (0, 1, 1/4), (3/4, 1, 1), (1, 0, 3/4), or any configuration equivalent by symmetry.
In general, let 
be the edge of the largest 
-dimensional cube that fits inside an 
-dimensional cube, with 
. Then
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
 |  |  |
(4)
|
(Croft et al. 1991, p. 53). For larger 
, little is known.
