In
recreational mathematics
Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research and application-based professional activity or as a part of a student's formal education. Although it is not necessarily limited ...
, a pandiagonal magic cube is a
magic cube
In mathematics, a magic cube is the dimension, 3-dimensional equivalent of a magic square, that is, a collection of integers arranged in an ''n'' × ''n'' × ''n'' pattern such that the sums of the numbers on each row, ...
with the additional property that all
broken diagonal In recreational mathematics and the theory of magic squares, a broken diagonal is a set of ''n'' cells forming two parallel diagonal lines in the square. Alternatively, these two lines can be thought of as wrapping around the boundaries of the squar ...
s (parallel to exactly two of the three coordinate axes) have the same sum as each other. Pandiagonal magic cubes are extensions of
diagonal magic cube The class of diagonal magic cubes is the second of the six magic cube classes (when ranked by the number of lines summing correctly), coming after the simple magic cubes.
In a diagonal magic cube of order ''m'',Traditionally, ''n'' has been used to ...
s (in which only the unbroken diagonals need to have the same sum as the rows of the cube) and generalize
pandiagonal magic square A pandiagonal magic square or panmagic square (also diabolic square, diabolical square or diabolical magic square) is a magic square with the additional property that the broken diagonals, i.e. the diagonals that wrap round at the edges of the squa ...
s to three dimensions.
In a pandiagonal magic cube, all 3''m'' planar arrays must be
panmagic square A pandiagonal magic square or panmagic square (also diabolic square, diabolical square or diabolical magic square) is a magic square with the additional property that the broken diagonals, i.e. the diagonals that wrap round at the edges of the squar ...
s. The 6 oblique squares are always
magic
Magic or Magick most commonly refers to:
* Magic (supernatural), beliefs and actions employed to influence supernatural beings and forces
* Ceremonial magic, encompasses a wide variety of rituals of magic
* Magical thinking, the belief that unrela ...
. Several of them may be panmagic squares.
A proper pandiagonal magic cube has exactly 9''m''
2 lines plus the 4 main triagonals summing correctly (no broken triagonals have the correct sum.)
The smallest pandiagonal magic cube has order 7.
See also
*
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 ...
References
*Hendricks, J.R; ''Magic Squares to Tesseracts by Computer'', Self-published 1999.
*Hendricks, J.R.; ''Perfect n-Dimensional Magic Hypercubes of Order 2n'', Self-published 1999.
Harvey Heinz: All about magic cubes
Magic squares
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