Cube Dissection
A Cube can be divided into 
subcubes for only 
, 8, 15, 20, 22, 27, 29, 34, 36, 38, 39, 41, 43, 45, 46, and
(Sloane's A014544).
The seven pieces used to construct the 
cube dissection known as the Soma Cube areone 3-Polycube and six 4-Polycubes (
), illustrated above.
Another cube dissection due to Steinhaus uses three 5-Polycubes andthree 4-Polycubes (
), illustrated above.
It is possible to cut a 
Rectangle into two identical pieces which will form a Cube (withoutoverlapping) when folded and joined. In fact, an Infinite number of solutions to this problem were discovered byC. L. Baker (Hunter and Madachy 1975).
References
Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, pp. 112-113, 1987. Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 203-205, 1989. Gardner, M. ``Block Packing.'' Ch. 18 in Time Travel and Other Mathematical Bewilderments. New York: W. H. Freeman, pp. 227-239, 1988. Gardner, M. Fractal Music, Hypercards, and More: Mathematical Recreations from Scientific American Magazine. New York: W. H. Freeman, pp. 297-298, 1992. Honsberger, R. Mathematical Gems II. Washington, DC: Math. Assoc. Amer., pp. 75-80, 1976. Hunter, J. A. H. and Madachy, J. S. Mathematical Diversions. New York: Dover, pp. 69-70, 1975. Sloane, N. J. A. Sequence A014544in ``The On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html.
- Combination Lock
- Combinatorial Species
- Combinatorial Topology
- Combinatorics
- Comma Derivative
- Comma of Didymus
- Comma of Pythagoras
- Common Cycloid
- Common Residue
- Commutation Coefficient
- Commutative
- Commutative Algebra
- Commutator
- Compact Group
- Compact Manifold
- Compactness Theorem
- Compact Set
- Compact Space
- Compact Surface
- Companion Knot
- Comparability Graph
- Comparison Test
- Compass
- Compatible
- Complementary Angle