A pandiagonal semiperfect magic cube is a semiperfect magic cube that remains semiperfect 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).
There is no pandiagonal semiperfect magic cube of order 3 (Benson and Jacoby 1988, p. 14).
The order 4 and 5 magic cubes shown above are pandiagonal semiperfect magic (Benson and Jacoby 1988, pp. 15-23 and 30).
