Supercube

Joseph Arkin, David C. Arney, Lee S. Dewald and Frank R. Giordano

A chapter in Applications of Fibonacci Numbers, 1991, pp 17-32 from Springer

Abstract: Abstract (1) In 1888, the first perfect magic cube ever constructed was of order 8, and was placed in “The Memoirs of the National Academy of Science” [3]. (2) Martin Gardner defines a perfect magic cube as follows: “A perfect magic cube is a cubical array of positive integers from 1 to N3 such that every straight line of N cells adds up to a constant. These lines include the orthogonals (the lines parallel to an edge), the two main diagonals of every orthogonal cross section and the four space diagonals. The constant is $$ (1 + 2 + 3 +... + {N^3})/{N^2} = \frac{1}{2}({N^4} + N)"[4]. $$ (3) E. G. Straus, in 1976, in a private letter to Arkin, described how he constructed a 7x7x7 perfect magic cube. This may be the lowest possible order of a perfect Latin 3-cube [5]. (4) In 1985, Arkin superimposed 6 orthogonal Latin cubes of order 7 to form 20 separate Latin 3-cubes [1]. (5) A perfect 4-dimensional hypercube of order 7 was constructed at West Point in 1989 [2].

Date: 1991
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DOI: 10.1007/978-94-011-3586-3_3

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