Recent research has examined the difficulties encountered when attempting to apply two-dimensional repeating designs to wrap around the surface of polyhedra. The study was concerned with symmetry in pattern but did not consider symmetries that involve a color change. A pattern is said to have color symmetry when it exhibits, as a minimum, one symmetry that is color-changing. Counterchange designs are produced when the color-changing symmetries of a pattern involve only two colors. This paper discusses the problems involved in the application of counterchange patterns to polyhedra, focusing particular attention on the icosahedron.