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 and "B" Petrie polygon projections (2("n" − 1) and "n" dihedral symmetry) of the related polytope which can include overlapping edges and vertices. Halved cube graph In graph theory, the halved cube graph or half cube graph of order "n" is the graph of the demihypercube, formed by connecting pairs of vertices at distance exactly two from each other in the hypercube graph. That is, it is the half-square of the hypercube. This connectivity pattern produces two isomorphic graphs, disconnected from each other, each of which is the halved cube graph. The construction of the halved cube graph can be