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
Compound of 5-cube and 5-orthoplex cells and edges. Mid-edges of the 5-cube cross mid-cell in the 16-cell, and vice versa. It can be seen as the 5-dimensional analogue of a compound of cube and octahedron. The 42 Cartesian coordinates of the vertices of the compound are. The convex hull of the vertices makes the dual of rectified 5-orthoplex. The intersection of the 5-cube and 5-orthoplex compound is the uniform birectified 5-cube: = ∩ . The compound can be seen in projection as the union of the two polytope graphs. The convex hulll as the dual of the rectified 5-orthoplex will have the same vertices, but