I have been using the following notation for the 4x4 cube:

Name the faces L, R, F, B, U, D. This follows the 3x3 notation. The inner
edges are then l, r, f, b, u, d. The front, upper, right quadrant
consists of one corner cube, FUR, two edge cubes, FUr and FRu, and one
center cube, fur.

Moves follow 3x3 notation: F moves the front face clockwise, f moves
the front slice clockwise. F' moves counterclockwise.

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The remainder of this message describes two processes for the 4x4 cube.

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The following process rotates three edge cubes. It preserves parity.

(FUl UBl URb)		l' RUR'U' L URU'R'

The following process rotates three center cubes. It can be used to
move one center cube between two faces.

(Ful Ulb Urb)		l' rur'u' l uru'r'

While the center process is sufficient, the edge process will not
organize all edges. It can easily be extended to a process that
moves (FUl to UBl) but that process messes up centers, corners, and
other edges. It also does not do 4-way moves. So the bloody thing
still takes an hour.

Martin Minow
decvax!minow@berkeley