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 1981, p. 14).
The order 4 and 5 magic cubes shown above are pandiagonal semiperfect magic cubes with magic constants 130 and 315, respectively
(Benson and Jacoby 1981, pp. 15-23 and 30).
The order-4 example is also compact: every adjacent block in a plane parallel
to a face, including blocks that wrap around the array,
sums to 130 (Duangmoon et al. 2022, p. 3). For example, the upper-left
block in the first layer has sum.
plane sections becomes 
, 
, 
, ..., or 
(Benson and Jacoby 1981, p. 4).
block in a plane parallel
to a face, including blocks that wrap around the array,
sums to 130 (Duangmoon et al. 2022, p. 3). For example, the upper-left
block in the first layer has sum 
.
