definition and a table Proper: A proper magic cube is a magic cube belonging to one of the six classes of magic cube, but containing exactly the minimum requirements for that class of cube. i.e. a proper simple or pantriagonal magic cube would contain no magic squares, a proper diagonal magic cube would contain exactly 3m + 6 simple magic squares, etc. This term was coined by Mitsutoshi Nakamura in April, 2004. Notes for table For the diagonal or pandiagonal classes, one or possibly 2 of the 6 oblique magic squares may be pandiagonal magic. All but 6 of the oblique squares are 'broken'. This is analogous to the broken diagonals in a pandiagonal magic square. i.e. Broken diagonals are 1-D in a 2-D square; broken oblique squares are 2-D in a 3-D cube. The table shows the minimum lines or squares required for each class (i.e. proper). Usually there are more, but not enough of one type to qualify for the next class. See also Magic hypercube Nasik magic hypercube Panmagic square Space diagonal John R. Hendricks References Further reading Frost, Dr. A. H., On the General Properties of Nasik Cubes, QJM 15, 1878, pp 93–123 Planck, C., The Theory of Paths Nasik, Printed for private circulation, A.J. Lawrence, Printer, Rugby,(England), 1905 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., Magic Squares to Tesseracts by Computer, Self-published 1999. 0-9684700-0-9 Hendricks, John R., Perfect n-Dimensional Magic Hypercubes of Order 2n, Self-published 1999. 0-9684700-4-1 Clifford A. Pickover (2002). The Zen of Magic Squares, Circles and Stars. Princeton Univ. Press, 2002, 0-691-07041-5. pp 101–121 External links Cube classes Christian Boyer: Perfect Magic Cubes Harvey Heinz: Perfect Magic Hypercubes Harvey Heinz: 6 Classes of Cubes Walter Trump: Search for Smallest Most perfect cube Perfect Cube Aale de Winkel: Magic Encyclopedia A long quote from C. Plank (1917) on the subject of nasik as a substitute term for perfect. Tesseract Classes The Square, Cube, and Tesseract Classes Magic squares