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Perfect magic cube
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==An alternative definition== In recent years{{when|date=June 2021}}, an alternative definition for the perfect magic cube was proposed by [[John R. Hendricks]]. By this definition, a perfect magic cube is one in which all possible lines through each cell sum to the magic constant. The name [[Nasik magic hypercube]] is another, unambiguous, name for such a cube. This definition is based on the fact that a [[pandiagonal magic square]] has traditionally been called 'perfect', because all possible lines sum correctly.<ref name=":0">{{Cite web|url=http://www.magic-squares.net/magic_cubes_index.htm|title=Magic Cubes Index Page|website=www.magic-squares.net|access-date=2016-12-04}}</ref> This same reasoning may be applied to [[hypercube]]s of any dimension. Simply stated; in an order ''m'' magic hypercube, if all possible lines of ''m'' cells sum to the magic constant, the hypercube is perfect. All lower dimension hypercubes contained in this hypercube will then also be perfect. This is not the case with the original definition, which does not require that the planar and diagonal squares be a [[pandiagonal magic cube]]. For example, a magic cube of order 8 has 244 correct lines by the ''old'' definition of "perfect", but 832 correct lines by this ''new'' definition. The smallest perfect magic cube has order 8, and none can exist for double odd orders. Gabriel Arnoux constructed an order 17 perfect magic cube in 1887. F.A.P.Barnard published order 8 and order 11 perfect cubes in 1888.<ref name=":1">{{Cite web|url=http://www.magic-squares.net/c-t-htm/C_timeline.htm|title=Magic Cube Timeline|website=www.magic-squares.net|access-date=2016-12-04}}</ref> By the modern (given by [[John R. Hendricks|J.R. Hendricks]]) definition, there are actually six [[magic cube class|classes of magic cube]]; [[simple magic cube]]s, [[pantriagonal magic cube]]s, [[diagonal magic cube]]s, pantriagonal diagonal magic cubes, [[pandiagonal magic cube]]s, and perfect magic cubes.<ref name=":0" />
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