A benefit of this classification is that it is consistent for all orders and all dimensions of magic hypercubes.
The minimum requirements for a magic cube are: all rows, columns, pillars, and 4 space diagonals must sum to the same value.
Minimum correct summations required = 3m2 + 4 Each of the 3m planar arrays must be a simple magic square.
Therefore, all main and broken space diagonals sum correctly, and it contains 3m planar simple magic squares.
Minimum correct summations required = 7m2 + 6m All 3m planar arrays must be pandiagonal magic squares.
These two conditions combine to provide a total of 9m pandiagonal magic squares.
C. Planck (1905) redefined Nasik to mean magic hypercubes of any order or dimension in which all possible lines summed correctly.
i.e. Nasik is a preferred alternate, and less ambiguous term for the perfect class.Minimum correct summations required = 13m2.
Until about 1995 there was much confusion about what constituted a perfect magic cube (see the discussion under Diagonal).
Included below are references and links to discussions of the old definition With the popularity of personal computers it became easier to examine the finer details of magic cubes.
For example, John Hendricks constructed the world's first Nasik magic tesseract in 2000.
For dimension 2, The Pandiagonal Magic Square has been called perfect for many years.
In this dimension, there is no ambiguity because there are only two classes of magic square, simple and perfect.
In the case of 4 dimensions, the magic tesseract, Mitsutoshi Nakamura has determined that there are 18 classes.