Designed by Oskar van Deventer, made by Recent Toys International; the box this one came in says copyright DaMert Co. 2005.
(plastic, each edge is 3.5 inches)

Four balls each have a number of circular depressions that allow them to be packed tightly together inside a pyramid shaped cage. A ball can rotate only if it sits in the depressions of at least two other balls. The goal is to rotate the balls so that each side is a single color (red, green, blue, or yellow). Here are the other two sides:

By observing that the green and blue faces have only one depression, Jaap's Page observes that a relatively simple solution proceeds by solving green and blue first (to allow more depressions available for the remainder of the solution). That is, position the red-green-blue corner, then the green-blue-yellow corner, then the third planet on the blue side, and finally the remaining planet, where the last step may require some temporary rotations of the other balls.

Further Reading
Jaap's Page, from: