The Rubik's-Cube Design Problem

Hana M. Bizek
Bridges: Mathematical Connections in Art, Music, and Science (2000)
Pages 347–352


The design problem spans art and mathematics. Its subproblems make incursions into science. We begin by stating, what the problem is -- a set of algorithms .that enable us to create a three-dimensional, composite, pleasant, geometrical design on a set of Rubik's cubes. We explain parity pairs, which influence design symmetry. We actually construct a simple design, the Menger Sponge. We conclude this article with some observations about fractals. The nature of the Rubik's cube makes it possible to create designs which mimic fractals.