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The Five and Six Dimensional Magic Hypercubes of Order 3

Published online by Cambridge University Press:  20 November 2018

John R. Hendricks
John R. Hendricks*
Affiliation:
Montreal Weather Office, Canada
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A recent publication entitled "Magic Squares and Cubes", by W. S. Andrews, published by the Dover Publications, New York, is an excellent authoritative book on magic squares, and magic cubes. In fact, chapter XIV entitled "Magic Octrahedroids", has shown examples of the extension into four-dimensional space. Andrews' method seems to be that of extending symmetrical considerations, which he calls reversions, in forming higher dimensional forms of magic squares. Neither he, nor any other author, to the best of my knowledge, has extended magic squares to higher than four dimensions.

La Hire must be given full credit for his method of breaking down magic squares into component squares, and conversely constructing magic squares from component squares. The approach of this author is to extend La Hire's method for n-dimensional space by means of a relation:

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 5 , Issue 2 , May 1962 , pp. 171 - 189
Copyright
Copyright © Canadian Mathematical Society 1962

References

* Use 2-agonal for square, 3-agonal for cube, n-agonal for hypercube.

* Define an i-row to be a row parallel to the xi axis.