Rubik's Cube group by rotations of the centre pieces, the second solely by symmetries of the corners, and the third solely by symmetries of the edges. The latter two factors are examples of wreath products. The simple groups that occur as quotients in the composition series of the standard cube group (i.e. ignoring centre piece rotations) are formula_37, formula_38, formula_30 (7 times), and formula_31 (12 times). Rubik's Cube group The Rubik’s Cube group is a group formula_1 that represents the structure of the Rubik's Cube mechanical puzzle. Each element of the set formula_2 corresponds to a cube move, which is the effect of
Gear Cube another four gears out and replaces them with standard edges. As the amount of gears get fewer and fewer, the difficulty level rises. So four sides can make 90° turns whereas the fifth and sixth sides are using the gear cogs giving only one option being a 180° turn. Gear Ball: This cube has two sets of edges. The outer edges are gear shaped with six teeth, and a black barrier on it. The inner edges are smaller and not circular, and only have too teeth. In addition, the corners have a three-pronged barrier. This cube is manufactured by Mefferts,