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
How Does a Moment Last Forever marks the first collaboration between Menken and Rice in over two decades; the last time they worked together had been in the "Beauty and the Beast" musical. Menken believes that the songs he and Rice had written for the musical would not have translated well to the screen due to the structural differences between the two formats. One of at least nine significant changes made to the film specifically for the remake, "How Does a Moment Last Forever" was conceived to explain Belle's backstory. Her quest to find out her mother's fate serves, in the plot, as a foundation for