The "Mystic IQ Puzzle" is similar to the "Chromo Ball" shown on:http://www.virtualpuzzlemuseum.com/roundpuzzles7of9.htm
The variation is that the faces are labelled with letters, making the position and orientation of the squares important.
What I didn't realize when I purchased one, and even then not until my wife discovered it while scrambling it, is that the 6 colored discs (and contained pieces) turn. This vastly simplifies the basic color-grouping puzzle relative to the Equator since local changes can be made to group the colors - you can focus on one face at a time and scrambling of an already solved face is minimal.
The Equator, Mozaika, and Chromo thus form an interesting family tree.