3-D generalization of the Polyominoes to -D. The number of polycubes composed of Cubes are 1, 1, 2, 8, 29, 166, 1023, ... (Sloane's A000162, Ball and Coxeter 1987).
See also Conway Puzzle, Cube Dissection, Diabolical Cube, Slothouber-Graatsma Puzzle, Soma Cube
References
Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, pp. 112-113, 1987.
Gardner, M. The Second Scientific American Book of Mathematical Puzzles & Diversions: A New Selection. New York:
Simon and Schuster, pp. 76-77, 1961.
Gardner, M. ``Polycubes.'' Ch. 3 in Knotted Doughnuts and Other Mathematical Entertainments. New York:
W. H. Freeman, 1986.
Sloane, N. J. A. Sequence
A000162/M1845
in ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.
The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.
© 1996-9 Eric W. Weisstein