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Pantriagonal Magic CubeA Pantriagonal Magic Cube is a magic cube where all 4m2 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 AND/OR pandiagonal magic squares, but not enough to satisfy any other classifications. Order 4 is the smallest Pantriagonal Magic Cube possible. References: Heinz, H.D. and Hendricks, J. R., Magic Square Lexicon: Illustrated. Self-published, 2000, 0-9687985-0-0. Pickover, Clifford A., The Zen of Magic Squares, Circles and Stars, Princeton Univ. Press, 2002, 0-691-07041-5 page 178. 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. J.R.Hendricks, Inlaid Magic Squares and Cubes 2nd Edition, 2000, 0-9684700-3-3. Pickover, Clifford A., The Zen of Magic Squares, Circles and Stars, Princeton Univ. Press, 2002, 0-691-07041-5 Pages 97,121,175,268. http://home.wanadoo.nl/aaledewinkel/Encyclopedia/ Aale de Winkel: Magic Encyclopedia http://members.shaw.ca/hdhcubes/cube_perfect.htm Harvey Heinz: Perfect Magic Hypercubes
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