From these some equivilences may be deduced: DL'F'D2R'D'R = L'D2F' = BD'B'D2L'F'D DF'R'DRD'FD' = FL'F'L =D'LD'BDB'L'D FR'F'RUF' = U'RUR'F'U = UF'L'ULU' Unfortunatly these equivilences only generate the 3 identities of length 12 , using the idea that midpoint of an identity must be the unique maximum along the path of the transform.