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 squares and/or pandiagonal magic squares, but not enough to satisfy any other classifications.

The constant for magic cubes is "S" = "m"("m"³ + 1)/2.

A proper pantriagonal magic cube has 7"m"² lines summing correctly. It contains "no" magic squares.

Order 4 is the smallest pantriagonal magic cube possible. A pantriagonal magic cube is the 3-dimensional equivalent of the pandiagonal magic square. Only, instead of the ability to move a line from one edge to the opposite edge of the square with it remaining magic, you can move a plane from one edge to the other.

ee also

* Magic cube classes
* triagonal

References

Further reading

* Heinz, H.D. and Hendricks, J. R., Magic Square Lexicon: Illustrated. Self-published, 2000, 0-9687985-0-0.
* Hendricks, John R., The Pan-4-agonal Magic Tesseract, The American Mathematical Monthly, Vol. 75, No. 4, April 1968, p. 384.
* Hendricks, John R., The Pan-3-agonal Magic Cube, Journal of Recreational Mathematics, 5:1, 1972, pp51-52.
* Hendricks, John R., The Pan-3-agonal Magic Cube of Order-5, JRM, 5:3, 1972, pp 205-206.
* Hendricks, John R., Pan-n-agonals in Hypercubes, JRM, 7:2, 1974, pp 95-96.
* Hendricks, John R., The Pan-3-agonal Magic Cube of Order-4, JRM, 13:4, 1980-81, pp 274-281.
* Hendricks, John R., Creating Pan-3-agonal Magic Cubes of Odd Order, JRM, 19:4, 1987, pp 280-285.
* Hendricks, J.R., "Inlaid Magic Squares and Cubes" 2nd Edition, 2000, 0-9684700-3-3.
* Clifford A. Pickover (2002). "The Zen of Magic Squares, Circles and Stars". Princeton Univ. Press. 0-691-07041-5 page 178.

External links

*http://home.wanadoo.nl/aaledewinkel/Encyclopedia/ Aale de Winkel: Magic Encyclopedia
*http://members.shaw.ca/hdhcubes/cube_perfect.htm Harvey Heinz: Perfect Magic Hypercubes