"

Since the corners are affected by the move F like

F = {1, 2, 3, 4} {5} {6} {7} {9}

the sequence FRBL does

FRBL = {1, 7} {2, 4} {3, 6} {5, 8}

that is, four 2-cycles so FRBL2 will return the corners to their original combination (ignoring twists - for now).  For the edges,

FRBL = {1, 2, 3, 5, 6, 8, 9, 11, 12} {4, 10, 7}

a 9-cycle and a 3-cycle.  The lowest common multiple (LCM) of a 9-cycle and a 3-cycle is a 9-cycle, hence the edges will be returned to their original combination by FRBL9 (ignnoring flips).

The LCM of a 2-cycle and a 9-cycle is a 18-cycle hence 

M = FRBL18 (72 moves)

is required to return both corners and edges to their original combination.  However, if they do not return with the correct twists and flips (haven't checked, can't be bothered, too much effort, but I seem to remember - from my now highly unreliable memory - that when I actually tried this move over 30 years ago it did twist and flip) then the sequence will have to be repeated to correct this.  Twists are 3-cycles and flips are 2-cycles.  The LCM of both is a 6-cycle, hence

M6 = FRBL108 (432 moves) = {∅}

A tediously long sequence but obviously much less than a complete solution since only 432 different positions are achieved. [[User talk:Spinningspark|Spark]]''' "