Pandiagonal magic cube
Encyclopedia
In a Pandiagonal magic cube, all 3m planar arrays must be panmagic square
s. The 6 oblique squares are always magic. Several of them may be panmagic squares.
Gardner called Langman’s pandiagonal magic cube a ‘perfect’ cube, presumably not realizing it was a higher class then Myer’s diagonal magic cube. A diagonal magic cube
has 3m plus 6 simple magic square
s.
A pandiagonal magic cube has 3m panmagic square
s and 6 simple magic square
s (one or two of these MAY be pandiagonal). A perfect magic cube
has 9m panmagic squares.
A proper pandiagonal magic cube has exactly 9m2 lines plus the 4 main triagonals summing correctly. (NO broken triagonals sum correct.)
Order 7 is the smallest possible pandiagonal magic cube.
Panmagic square
A pandiagonal magic square or panmagic square is a magic square with the additional property that the broken diagonals, i.e...
s. The 6 oblique squares are always magic. Several of them may be panmagic squares.
Gardner called Langman’s pandiagonal magic cube a ‘perfect’ cube, presumably not realizing it was a higher class then Myer’s diagonal magic cube. A diagonal magic cube
Diagonal magic cube
A Diagonal Magic Cube is an improvement over the simple magic cube. It is the second of six magic cube classes when ranked by the number of lines summing correctly....
has 3m plus 6 simple magic square
Simple magic square
A simple magic square is the lowest of two basic classes of magic square. It has the minimum requirements for a square to be considered magic. All lines parallel to the edges, plus the two main diagonals must sum to the magic constant...
s.
A pandiagonal magic cube has 3m panmagic square
Panmagic square
A pandiagonal magic square or panmagic square is a magic square with the additional property that the broken diagonals, i.e...
s and 6 simple magic square
Simple magic square
A simple magic square is the lowest of two basic classes of magic square. It has the minimum requirements for a square to be considered magic. All lines parallel to the edges, plus the two main diagonals must sum to the magic constant...
s (one or two of these MAY be pandiagonal). A perfect magic cube
Perfect magic cube
In mathematics, a perfect magic cube is a magic cube in which not only the columns, rows, pillars and main space diagonals, but also the cross section diagonals sum up to the cube's magic constant....
has 9m panmagic squares.
A proper pandiagonal magic cube has exactly 9m2 lines plus the 4 main triagonals summing correctly. (NO broken triagonals sum correct.)
Order 7 is the smallest possible pandiagonal magic cube.