Generalized For All Dimensions
A magic hypercube of dimension n is perfect if all pan-n-agonals sum correctly. Then all lower dimension hypercubes contained in it are also perfect.
For dimension 2, The Pandiagonal Magic Square has been called perfect for many years. This is consistent with the perfect (nasik) definitions given above for the cube. 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. He has determined their characteristics and constructed examples of each. And in this dimension also, the Perfect (nasik) magic tesseract has all possible lines summing correctly and all cubes and squares contained in it are also nasik magic.
Read more about this topic: Magic Cube Classes
Famous quotes containing the words generalized and/or dimensions:
“One is conscious of no brave and noble earnestness in it, of no generalized passion for intellectual and spiritual adventure, of no organized determination to think things out. What is there is a highly self-conscious and insipid correctness, a bloodless respectability submergence of matter in manner—in brief, what is there is the feeble, uninspiring quality of German painting and English music.”
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