Soma Cube

A solid Quantum Mechanics byWerner Heisenberg. There are seven soma pieces composed of all the irregularface-joined cubes (Polycubes) with cubes. The object is to assemble the pieces into aCube. There are 240 essentially distinct ways of doing so (Beeler et al. 1972, Berlekamp et al. 1982), asfirst 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 ofthe cube, three ways of assembling the black piece, and ways of assembling the green, orange, white, red, and bluepieces are counted, the total number of solutions rises to 1,105,920.

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.; Gosper, R. W.; and Schroeppel, R. HAKMEM. Cambridge, MA: MIT Artificial Intelligence Laboratory, Memo AIM-239, Item 112, Feb. 1972.

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.

Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 203-205, 1989.

Gardner, M. Ch. 6 in The Second Scientific American Book of Mathematical Puzzles & Diversions: A New Selection. New York: Simon and Schuster, pp. 65-77, 1961.

Steinhaus, H. Mathematical Snapshots, 3rd American ed. New York: Oxford University Press, pp. 168-169, 1983.

• Link
• Linkage
• Link Diagram
• Linking Number
• Links Curve
• Linnik's Constant
• Linnik's Theorem
• Lin's Method
• Liouville Function
• Liouville Measure
• Liouville Number
• Liouville Polynomial Identity
• Liouville-Roth Constant
• Liouville's Boundedness Theorem
• Liouville's Conformality Theorem
• Liouville's Conic Theorem
• Liouville's Constant
• Liouville's Elliptic Function Theorem
• Liouville Space
• Liouville's Phase Space Theorem
• Liouville's Rational Approximation Theorem
• Liouville's Sphere-Preserving Theorem
• Lipschitz Condition
• Lipschitz Function
• Lipschitz's Integral