Polycube

3-D generalization of the Polyominoes to $n$-D. The number of polycubes $N(n)$ composed of $n$ 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.