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
Halved cube graph in the original graph. For instance, the halved cube graph of order four may be formed from an ordinary three-dimensional cube by keeping the cube edges and adding edges connecting pairs of vertices that are on opposite corners of the same square face. The halved cube graph formula_2 of order 3 is the complete graph "K", the graph of the tetrahedron. The halved cube graph formula_3 of order 4 is "K", the graph of the four-dimensional regular polytope, the 16-cell. The halved cube graph formula_4 of order five is sometimes known as the Clebsch graph, and is the complement of