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 between. - Place those two edges on the top side and complete the following algorithm: (U2 R4) 2. Step 2: Repeat the previous step until all edge pieces are in the correct position (edge colors match the colors of the sides it is between). Phase 3: Orient the edges: (second algorithm used) Step 1: Rotate all sides until the cube is back in a cubic state using the following algorithm: R4 (repeat as necessary). There are multiple variations of the Gear Cube, ranging from the most simple, a 2x2 Gear Shift, to the most complicated, the 3x3 Even Less Gears