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 different edges. Compound of 5-cube and 5-orthoplex In 5-dimensional geometry, the 5-cube 5-orthoplex compound is a polytope compound composed of a regular 5-cube and dual regular 5-orthoplex. A "compound polytope" is a figure that is composed of several polytopes sharing a common center. The outer vertices of a compound can be connected to form a convex polytope called the convex hull. The compound is a facetting of the convex hull. In 5-polytope compounds constructed as dual pairs, the hypercells and vertices swap positions and cells and edges swap positions. Because of this the number of hypercells and vertices are equal,