Editing Magic hypercube (section)

==Perfect magic hypercubes==
{{see also|Magic Cube Classes}}
If, in addition, the numbers on every [[cross section (geometry)|cross section]] diagonal also sum up to the hypercube's magic number, the hypercube is called a '''perfect magic hypercube'''; otherwise, it is called a '''semiperfect magic hypercube'''. The number ''n'' is called the order of the magic hypercube.

This definition of "perfect" assumes that one of the older definitions for perfect magic cubes is used. The '''''Universal Classification System for Hypercubes''''' (John R. Hendricks) requires that for any dimension hypercube, ''all'' possible lines sum correctly for the hypercube to be considered ''perfect'' magic. Because of the confusion with the term ''perfect'', '''''nasik''''' is now the preferred term   for ''any'' magic hypercube where '''''all''''' possible lines sum to ''S''. Nasik was defined in this manner by C. Planck in 1905. A nasik magic hypercube has {{sfrac|2}}(3<sup>''n''</sup> &minus; 1) lines of ''m'' numbers passing through each of the ''m''<sup>''n''</sup> cells.