\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2010f.00009}
\itemau{Heinz, Harvey D.}
\itemti{Hypercube classes -- an update.}
\itemso{J. Recreat. Math. 35(2006), No. 1, 5-10 (2009).}
\itemab
From the introduction: A magic hypercube is a recta-linear array of numbers arranged in such a way that all orthogonal lines plus the so-called diagonals sum to a constant. A magic square is a magic hypercube of dimension 2, a cube is a magic hypercube of dimension 3, a magic tesseract is one of dimension 4, and so on. A recent article described a system developed around 1990 for classifying magic hypercubes according to types of lines that summed correctly. The article mentions that there are two classes of this type for the magic square, simple and pandiagonal (Nasik). It then goes on to define five classes for the magic cube. This article will define a sixth (and final) class for the cube and propose several name changes. A following article will present the definitions for the 18 classes of magic tesseracts.
\itemrv{~}
\itemcc{A20 K20}
\itemut{recreational mathematics; multidimensional magic squares; diagonal sums; classification system for magic cubes; history of perfect magic cubes}
\itemli{}
\end