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
Centered cube number Centered cube number A centered cube number is a centered figurate number that counts the number of points in a three-dimensional pattern formed by a point surrounded by concentric cubical layers of points, with "i" points on the square faces of the "i"-th layer. Equivalently, it is the number of points in a body-centered cubic pattern within a cube that has "n" + 1 points along each of its edges. The first few centered cube numbers are The centered cube number for a pattern with "n" concentric layers around the central point is given by the formula The same number