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In recreational mathematics, a pandiagonal magic cube is a magic cube with the additional property that all broken diagonals (parallel to exactly two of the three coordinate axes) have the same sum as each other. Pandiagonal magic cubes are extensions of diagonal magic cubes (in which only the unbroken diagonals need to have the same sum as the rows of the cube) and generalize pandiagonal magic squares to three dimensions.
In a pandiagonal magic cube, all 3m planar arrays must be panmagic squares. The 6 oblique squares are always magic. Several of them may be panmagic squares.
A proper pandiagonal magic cube has exactly 9m2 lines plus the 4 main space diagonals summing correctly (no broken space diagonals have the correct sum.)
The smallest pandiagonal magic cube has order 7.
and 12 Related for: Pandiagonal magic cube information
In recreational mathematics, a pandiagonalmagiccube is a magiccube with the additional property that all broken diagonals (parallel to exactly two of...
the magiccube. If the sums of numbers on a magiccube's broken space diagonals also equal the cube'smagic number, the cube is called a pandiagonal magic...
then Myer’s cube. See previous note re Boyer and Trump. The smallest normal pandiagonalmagiccube is order 7; see Pandiagonalmagiccube. Minimum correct...
A pandiagonalmagic square or panmagic square (also diabolic square, diabolical square or diabolical magic square) is a magic square with the additional...
of magiccubes may contain some simple magic squares and/or pandiagonalmagic squares, but not enough to satisfy any other classifications. The magic constant...
correct lines and 9m pandiagonalmagic squares. Magiccube classes Traditionally, n has been used to indicate the order of the magic hypercube. However...
pandiagonal, and an order-8 cube we class as pantriagonal. In another 1878 paper he showed another pandiagonalmagiccube and a cube where all 13m lines sum...
Cubes (1878), On the construction of Nasik Squares of any order (1896). He showed that it is impossible to have normal singly-even pandiagonalmagic squares...
pandiagonalmagic squares", in: Mathematics Today, 1998, vol. 34, pp. 139–143. ISSN 1361-2042. D. S. Brée and K. M. Ollerenshaw, "Pandiagonalmagic-squares...
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