What are pandiagonal perfect multiplicative magic cubes?
As explained in the multiplicative magic cubes page, a pandiagonal perfect magic cube has all its lines (rows, columns, pillars, triagonals, plane diagonals, broken triagonals and broken diagonals) magic. It is a perfect magic cube that remains perfect magic when any face of the cube is moved parallel to itself, from its side to the opposite side of the cube. They are the BEST possible cubes: any line, entire or broken, in any direction gives always the same product! Because a cell in a cube has 3^3 – 1 = 26 adjacent cells, a pandiagonal perfect multiplicative magic cube of order n has all its 13n lines which are magic. My 4 best pandiagonal perfect multiplicative magic cubes, extracted from the general table, are: Order Magic product P Max nb Comments 8 89518183823250314294722560000 (~ 8.95 E+28) 17 297 280 The best known pandiag. perfect magic cube (of any order) using the smallest P 9 265237261271449982022984892416000 (~ 2.65 E+32) 591 192 The best known 9th-order pandiag. perfect m
