A catalog of skewb moves

      The goal here is to collect enough moves to support the following 
  solution strategy: fix the centers and solve the corners using 
  "clean corner moves" (i.e., moves which do not effect the centers).

      The basic moves are twists by 120 degrees clockwise about
  each of the six corners FRU,FLU,BRU,BLU,BDR,BDL,DFR,DFL. The 
  inverse of a move m will be denoted m^(-1) and the composition of
  two moves m1, m2 will be denoted m1*m2 (move m1 first, then m2).

      Let [a,b]=a*b*a^(-1)*b^(-1), 

    5. FRU*BLU*FRU^(-1) is order 3.

    6. [FRU*FLU]^3 twists 6 the corners clockwise by 120 degrees. The
       2 corners not twisted are those opposite the FRU, FLU corners: the 
       BDR, BDL corners and the centers are all left fixed.
      (FRU*FLU)^3 = (FLU*FRU)^3 rotates all the corners except for the 
       bd corners. It does not permute any facets.

    7. This move, [FRU*BLU]^5, fixes all the centers and the 2 "opposite" 
       corners: DFL, BDR. It twists the 3 corners FLU, BLU, and FRU. On 
       the remaining 3 corners, it acts as the permutation  (DFR,BRU,BDL). 

    8. FRU = BDL (actually, they are only equal up to a rotatation of
       the entire cube). In general, a corner move is equal to the 
       opposite corner move up to a rotation of the entire cube.

    10. (FRU*FLU)^3*(BDL*BDR)^6 rotates all the corners except for
        the bu and the df corners. It does not permute any facets.
        (FRU*FLU)^6*(BDL*BDR)^3 is the same move, but rotates in the
        opposite direction.

    11. (FRU*FLU)^6*(BDL*BDR)^6 rotates the 4 bottom corners. It 
        does not permute any facets.

    12. (FRU*FLU)^6*(BDL*BDR)^3*(DFR*DFL)^3 rotates the 4 front 
        corners. It does not permute any facets.

    13. (BRU*FLU)^9 is a 5 cycle on the center facets. It fixes
        the bottom and does not affect any corners.
        (BLU*FRU)^9 is a 5 cycle on the center facets. It fixes
        the bottom and does not affect any corners.

    14. (BLU*FRU)^9*(BRU*FLU)^9 is a product of 2 2-cycles on 
        the center facets, swapping front/back and up/right. 
        It fixes the bottom and does not affect any corners.

    15. bottomspin=(FRU*FLU)^6*(BDL*BDR)^3*(DFR*DFL)^3
        U=counterclockwise (wrt up face) rotation of entire 
          cube by 90 degrees
        bottomspin*U*bottomspin rotates but does not swap
        2 corners (the DFR and BDL) and does not affect any 
        other corners or faces.