Geodesic
The Five and Six Dimensional Magic Hypercubes of Order 3
Canadian mathematical bulletin, Tome 5 (1962) no. 2, pp. 171-189

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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: 
Hendricks, John R. The Five and Six Dimensional Magic Hypercubes of Order 3. Canadian mathematical bulletin, Tome 5 (1962) no. 2, pp. 171-189. doi: 10.4153/CMB-1962-019-x
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