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 are one 3-Polycube and six 4-Polycubes ( ), illustrated above.

Another cube dissection due to Steinhaus uses three 5-Polycubes and three 4-Polycubes ( ), illustrated above.

It is possible to cut a Rectangle into two identical pieces which will form a Cube (without overlapping) when folded and joined. In fact, an Infinite number of solutions to this problem were discovered by C. 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 A014544 in ``The On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html.

© 1996-9

1999-05-25