Nasik magic hypercube
A Nasik magic hypercube is a magic hypercube with the added restriction that all possible lines through each cell sum correctly to where S = the magic constant, m = the order and n = the dimension, of the hypercube.
Or, to put it more concisely, all pan-r-agonals sum correctly for r = 1...n.
The above definition is the same as the Hendricks definition of perfect, but different from the Boyer/Trump definition. See Perfect magic cube
A Nasik magic cube is a magic cube with the added restriction that all 13m2 possible lines sum correctly to the magic constant. This class of magic cube is commonly called perfect (John Hendricks definition.). See Magic cube classes. However, the term perfect is ambiguous because it is also used for other types of magic cubes. Perfect magic cube demonstrates just one example of this.
The term nasik would apply to all dimensions of magic hypercubes in which the number of correctly summing paths (lines) through any cell of the hypercube is P = (3n- 1)/2
A pandiagonal magic square then would be a nasik square because 4 magic line pass through each of the m2cells. This was A.H. Frost’s original definition of nasik.
A nasik magic cube would have 13 magic lines passing through each of its m3 cells. (This cube also contains 9m pandiagonal magic squares of order m.)
A nasik magic tesseract would have 40 lines passing through each of its m4 cells.
And so on.
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