Pandiagonal magic cube

Pandiagonal magic cube

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.

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 squares.

A pandiagonal magic cube has 3m panmagic squares and 6 simple magic squares (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.

ee also

*Magic cube classes

References

*Hendricks, J.R; "Magic Squares to Tesseracts by Computer", Self-published 1999. ISBN 0-9684700-0-9
*Hendricks, J.R.; "Perfect n-Dimensional Magic Hypercubes of Order 2n", Self-published 1999. ISBN 0-9684700-4-1
* [http://members.shaw.ca/hdhcubes/ Harvey Heinz: All about magic cubes]


Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать реферат

Look at other dictionaries:

  • Magic cube classes — Every magic cube may be assigned to one of six magic cube classes, based on the cube characteristics. This new system is more precise in defining magic cubes. But possibly of more importance, it is consistent for all orders and all dimensions of… …   Wikipedia

  • 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. Perfect magic cubes of order one are trivial;… …   Wikipedia

  • Magic cube — For the flashbulb cartridges, see Magicube. For the puzzle, see Rubik s Cube. In mathematics, a magic cube is the 3 dimensional equivalent of a magic square, that is, a number of integers arranged in a n x n x n pattern such that the sum of the… …   Wikipedia

  • Pantriagonal magic cube — A pantriagonal magic cube is a magic cube where all 4 m 2 pantriagonals sum correctly. There are 4 one segment, 12( m − 1) two segment, and 4( m − 2)( m − 1) three segment pantriagonals. This class of magic cubes may contain some simple magic… …   Wikipedia

  • 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. In a diagonal magic cube of order m, all 6m of the diagonals in the m planes… …   Wikipedia

  • Pantriagdiag magic cube — A Pantriagonal Diagonal magic cube is a magic cube that is a combination Pantriagonal magic cube and Diagonal magic cube. All main and broken triagonals must sum correctly, In addition, it will contain 3m order m simple magic squares in the… …   Wikipedia

  • Cube Magique — En mathématiques, un cube magique est l équivalent tridimensionnel d un carré magique, c’est à dire, un nombre d entiers arrangés dans un cube de taille n x n x n tels que la somme des nombres de chaque ligne d axe x, chaque ligne d axe y, et… …   Wikipédia en Français

  • Cube magique — En mathématiques, un cube magique est l équivalent tridimensionnel d un carré magique, c’est à dire, un nombre d entiers arrangés dans un cube de taille n x n x n tels que la somme des nombres de chaque ligne d axe x, chaque ligne d axe y, et… …   Wikipédia en Français

  • Nasik magic hypercube — A Nasik magic hypercube is a magic hypercube with the added restriction that all possible lines through each cell sum correctly to where S = the magic constant, m = the order and n = the dimension, of the hypercube. Or, to put it more concisely,… …   Wikipedia

  • Cube Magique Parfait — En mathématiques, un cube magique parfait est un cube magique dans lequel non seulement les nombres sur les axes x, sur les axes y, et sur les axes z et sur les diagonales spatiales principales, mais aussi la section plane diagonale ont pour… …   Wikipédia en Français

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”