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Soma Cube


SomaCube

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 <=4 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 2^5 ways of assembling the green, orange, white, red, and blue pieces are counted, the total number of solutions rises to 1105920.


See also

Cube Dissection, Polycube, SOMA

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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.

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Soma Cube

Cite this as:

Weisstein, Eric W. "Soma Cube." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SomaCube.html

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