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
Truncated cube The truncated triangular trapezohedron is another polyhedron which can be formed from cube edge truncation. The "truncated cube", is second in a sequence of truncated hypercubes: In the mathematical field of graph theory, a truncated cubical graph is the graph of vertices and edges of the "truncated cube", one of the Archimedean solids. It has 24 vertices and 36 edges, and is a cubic Archimedean graph. Truncated cube In geometry, the truncated cube, or truncated hexahedron, is an Archimedean solid. It has 14 regular faces (6 octagonal and 8 triangular), 36 edges, and 24 vertices. If the truncated cube has