6 x order 3 -> 4 3-cycles of edges (uf ur fr) (ul br df) (ub dr fl) (bl db dl) 6 x order 2 -> (uf db) (ul dr) (ub df) (ur dl) (fr bl) (fl br) 6 2-cycles of edges 6 x order 6 -> (uf bl ur db fr dl) (ul ub br dr df fl) 2 6-cycles of edges repeating --------- (L' R U' D)3 6x order 2 EDGE/2p 1 (X)1 (1:8 3:4) 3 250 6x order 3 CORNER/3p EDGE/0p CENTER/2p 1 (X)1 (1:12 3:6) 3 517 6x order 3 EDGE/2p CENTER/1o 1 (X2)1 (1:14 3:4) 3 250 6x order 3 (F' U' D L 2F' 2L' 2F 2L)11 6x order 3 (F' U' D L F Fv' B' L Lv' R' F' Fv B L' Lv R)11 6x order 3 (1-2F' 2L' 2F 2L U' D L)11 6x order 3 (2L B' 2L2 F 2D' 2F' 2D 2F Lv')4 6x order 3 ((D' 2F2 U 2F2)3 Lv' 2F )4 6x order 3 (U' 2F 2L 2F' 2L D R' L)4 6x order 3 (U' F' B Fv L' R Lv F B' U' D F D' U Fv' Lv)4 6x order 3 (U' F' B D' U L R' B' F L F' B Rv' Fv' )4 6x order 3 (U' F' B D' U L R' B' F L F' B Lv Fv')4 6x order 3 (48 moves) (R2 L3 D1 F2 R3 D3 F1 B3 U1 D3 F1 L1 D2 F3 R1 L2)2 6x order 3 (32 moves) (2F U 2F2 U D 2F2 D Lv 2F' U' 2F2 U' D' 2F2 U' Lv' U D')2 6x order 3 (32 moves) (F Lv Fv' L' B F' D' B2 F2 U R L' U' R2 L2 U)2 6x order 3 (28 moves) (D' 2L2 U 2L' 2F' Lv2 B' 2L2 F 2L' 2F')2 6x order 3 (20 slice moves) (D' 2L2 U 2L' F' 2F' R2 L2 F 2L' 2F')2 6x order 3 (22 slice moves) (U2 D2 B L U2 F' L' U D' L' R U B L2 U' F')2 6x order 3 (32 face moves) (F B2 R2 U L U L' R2 U' B U' D B' R' B' L U2 F)2 6x order 3 (36 face moves) (L2 U2 B' L R U D L2 R2 D2 F B R D2 F2)4 6x order 3 (60 face moves, base process is 15 moves) (F U L2 B' U' L R' U' D L F U2 L' F2 B L2 R2)2 6x order 3 (34 face moves) (L U D B2 L2 F' B' L' R' U2 F2 U)2 6x order 3 (24 face moves) (U2 F U' B R' U2 B D L B' D B2 L2 B2 R F2 D' F)2 6x order 3 ((R2 U3 R1 D1 F1 B1 R3 L3 U1 D1 F3 U1 F3 U2 D3 B2 R2 U1) 6x order 3 (B F D F B U D)6)4 This is mark pattern 1 combined with another pattern to create 6x order 3 EDGE/2p CENTER/1o 1 (X)1 (1:14 6:2) 6 250 6x order 6 (F1 R1 L3 U2 F2 B2 U3 D3 F1 B3 L3 U1 R2 L2 U2 F2 B2 D1)7 6x order 6 (F1 R1 L3 U2 F2 B2 U3 D3 F1 B3 L3 U1 R2 L2 U2 F2 B2 D1)5 6x order 6 (90 moves) 6 X order 3 solutions non-repeating ------------- // Rubik's Compendium Method // Earliest 6 X order 3 process R' L2 F2 B2 U2 R2 L2 F2 B2 D2 R' Fv' R' L2 F2 B2 U2 R2 L2 F2 B2 D2 R' Fv 2R' 2F' 2R 2F // Cube Games, page 26 B' R' L U' D F B' U2 R2 L2 F2 B2 D2 R D U2 F2 B2 R2 U2 D2 F2 B2 L2 D 25 moves Singmaster, Notes on Rubik's Magic Cube by R. Walker B' R's U's Fs U2 R2s F2s D2 R D U2 F2s R2 U2s F2s L2 D restated using sgn (twizzle) notation B' R' L U' D F B' U2 R2 L2 F2 B2 D2 R D U2 F2 B2 R2 U2 D2 F2 B2 L2 D Note that this matches the solution from Cube Games (R' L2 F2 B2' U2 R2 L2' F2 B2' D2 R' Uv)2 2L 2D' 2L' 2D R2 L' D F2 R' D' F B' U D' F L D2 F' R L2 16 moves 2F U 2F2 U2 2D2 2L2 U L 2F2 L2 2D2 L 2F' 2D2 2F D 2F2 2L2 D L' 2F2 2D2 L' U2 R2 2F U2 L2 2F 2D2 2L2 U 2F2 U2 2L2 U L 2F2 L2 2D2 L 2F' 14 slice moves 2F U 2F2 1-2U2 2L2 U L 2F2 L2 2U2 L 2F' 2U2 13 block moves (here we used face + slice + slab) ((D' 2F2 U 2F2)3 Lv')2 2F 2D 2F' 2D' mark's method for 6 x order 3 in fact (D' 2F2 U 2F2)3 is optimal in the <2F, U, D> subgroup restated without full cube rotations or slice moves: (F2 B2 D' F2 B2 D)3 (F2 B2 R' F2 B2 R)3 B F' D U' R L' B F' using < U, D, F, B, 2L, 2F, 2D > F 2F 2L2 F2 2D2 F 2L U 2F2 U2 2L2 U 2F' 2D' using < U, F, B, 2F, 2D > B 2D2 B' U B2 U' F 2D2 B' 2F 2D F' B U B2 2D' 2F2 U' 2F partial 6x order 3 pattern -------------------------- ((U F R)10 Fv' Uv')7 proceeds on to the complete pattern: ((U F R)10 Fv' Uv)35 ((U R F)12 Uv Fv')16 improvement ((U R')18 Uv Rv')35 using only 2 faces plus cube rotations using one 3 cycle of edges as a base ------------------------------------ ((R1 U2 (R1 U1)2 R2 U3 R3 U3 R2) Fv Uv' Rv2)10 (L2 D L D L2 (D' L')2 D2 L1' Fv Uv' Rv2)10 ((R1 U2 (R1 U1)2 R2 U3 R3 U3 R2) Fv Rv')10 (L2 D L D L2 (D' L')2 D2 L1' Fv Rv')10 220 moves (((R1 U2 (R1 U1)2 R2 U3 R3 U3 R2) Fv Rv') (L2 D L D L2 (D' L')2 D2 L1' Fv Rv'))8 176 moves (R U2 R U R U R2 U' R' U' R2 L2 D L D L2 D' L' D' L' D2 L' Fv Rv)8 176 moves (L' U' L U' R2 L' D L D R2 U2 L' U' Uv Fv)8 104 moves dik t winter's cube (early) solution F1 R1 L1 U1 D3 F1 B1 U2 D2 L1 D2 B2 U1 D1 B2 R2 U1 F2 B2 R2 L2 U1 L2 DeepCubeA's solution F D F B L R' U U B D U F' U' B' U B B R B' D' B' D F' D' B R B' R' B' D B F 32 moves efficientcube's solution R' D' F' B U' D' L' B2 U' R' D R' U' L' B' L F R L' U' L F D U' R' 25 moves (one simple edit) 6 X order 6 new type (6 X order 3 combined with 2 X) F U L2 B' D' L R' U D' L' R2 B U2 R' F' U2 D2 17 moves F U L2 B' D' L R' U D' L' R2 B U2 R' F' U2 D2; (uf fr dr db bl ul) (ub fl ur df br dl) [6] oddities -------- ((2F 2D2 2L2 U 2F2 U2 2L2 U L 2F2 L2 2D2 L 2F')24)3 this generates the 10 spot pattern on the megaminx using a 6x order 3 process as a part of the solution ASCII representation -------------------- 6 X order 3 TOP 0 2 0 2 0 2 0 2 0 LEFT FRONT RIGHT BACK 4 1 4 2 5 2 5 0 5 3 4 3 1 4 1 5 2 5 0 5 0 4 3 4 4 1 4 2 5 2 5 0 5 3 4 3 DOWN 1 3 1 3 1 3 1 3 1 6 X order 2 TOP 0 1 0 1 0 1 0 1 0 LEFT FRONT RIGHT BACK 4 5 4 2 3 2 5 4 5 3 2 3 5 4 5 3 2 3 4 5 4 2 3 2 4 5 4 2 3 2 5 4 5 3 2 3 DOWN 1 0 1 0 1 0 1 0 1