A pandiagonal perfect magic cube is a perfect magic cube that remains perfect when any single orthogonal section is "restacked"
cyclically so that the ordering of any set of 
plane sections becomes 
, 
, 
, ..., or 
(Benson and Jacoby 1981, p. 4).
Pandiagonal perfect magic cubes are possible for orders 8 and 9, but no smaller orders. They are also not possible for orders 12 or 14, but are possible for all orders that are multiples of 8 and odd orders greater than or equal to 9 (Benson and Jacoby 1981, p. 5). Benson and Jacoby (1981, pp. 76-78) explicitly construct a pandiagonal perfect magic cube of order 9.
Planck (1950; cited in Gardner 1988) constructed a perfect pandiagonal magic cube.
