Magic cube classes

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In mathematics, a magic cube of order ${\displaystyle n}$ is an ${\displaystyle n\times n\times n}$ grid of natural numbers satisying the property that the numbers in the same row, the same column, the same pillar or the same length-${\displaystyle n}$ diagonal add up to the same number. It is a ${\displaystyle 3}$-dimensional generalisation of the magic square. A magic cube can be assigned to one of six magic cube classes, based on the cube characteristics. A benefit of this classification is that it is consistent for all orders and all dimensions of magic hypercubes.