Soma Cube
A solid dissection puzzle invented by Piet Hein during a lecture on Quantum Mechanics by Werner Heisenberg. There are seven soma pieces
composed of all the irregular face-joined cubes (polycubes)
with 
cubes. The object is to assemble the pieces
into a cube. There are 240 essentially distinct ways of
doing so (Beeler 1972, Berlekamp et al. 1982), as first enumerated one rainy
afternoon in 1961 by J. H. Conway and Mike Guy.
A commercial version of the cube colors the pieces black, green, orange, white, red, and blue. When the 48 symmetries of the cube, three ways of assembling the black
piece, and 
ways of assembling the green, orange,
white, red, and blue pieces are counted, the total number of solutions rises to 
.
SEE ALSO: Cube Dissection,
Polycube,
SOMA
REFERENCES:
Albers, D. J. and Alexanderson, G. L. (Eds.). Mathematical People: Profiles and Interviews. Boston, MA: Birkhäuser, p. 43,
1985.
Ball, W. W. R. and Coxeter, H. S. M. Mathematical
Recreations and Essays, 13th ed. New York: Dover, pp. 112-113, 1987.
Beeler, M. Item 112 in Beeler, M.; Gosper, R. W.; and Schroeppel, R. HAKMEM. Cambridge, MA: MIT Artificial Intelligence Laboratory, Memo AIM-239, pp. 48-50,
Feb. 1972. http://www.inwap.com/pdp10/hbaker/hakmem/polyominos.html#item112.
Berlekamp, E. R.; Conway, J. H.; and Guy, R. K. Ch. 24 in Winning
Ways for Your Mathematical Plays, Vol. 2: Games in Particular. London:
Academic Press, 1982.
Bundgaard, T. "Thorleif's SOMA Page." http://www.fam-bundgaard.dk/SOMA/SOMA.HTM.
Cundy, H. and Rollett, A. Mathematical
Models, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 203-205, 1989.
Gardner, M. "Mathematical Games: A Game in Which Standard Pieces Composed of Cubes are Assembled into Larger Forms." Sci. Amer. 199, 182-192,
Sep. 1958.
Gardner, M. "The Soma Cube." Ch. 6 in The Second Scientific American Book of Mathematical Puzzles & Diversions: A New Selection.
New York: Simon and Schuster, pp. 65-77, 1961.
Maas, M. and Retina GbR. "3-D Soma Cube Online." http://www.retina.de/cube/somacube.html.
Steinhaus, H. Mathematical
Snapshots, 3rd ed. New York: Dover, pp. 168-169, 1999.
Referenced on Wolfram|Alpha:
Soma Cube
CITE THIS AS:
Weisstein, Eric W. "Soma Cube." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/SomaCube.html
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