(2R2' 2L 2R2' 2L2 2R2 2L' 2R2 2L2')6 ((U R2 Uv2 R' Uv' R Uv' U)6 Uv2)38 5 checkerboard, 1140 moves (U2' F2 U2 F' U F L2 F2 L2' F' U' F' U L2 F' L2' F2' U2 F2' U2' Fv)19 Lv' 5 checkerboard, 380 moves (U2 F2 R2' F2' U R' U2' F2 R2' F U2' F2 U' R2 U F2' U2 F2 R U' R2 U2' Uv2')12 5 checkerboard, 264 moves (F2 R2' F2' U R' U2' F2 R2' F U2' F2 U' R2 U F2' U2 F2 R U' R2 Uv2')12 5 checkerboard, 240 moves (F2 U2 F U2' R2' F U2 F2 R2 U' F2 U2' F2 R2' U2' F U' F2 R2 U2 R' U Rv)9 5 checkerboard, 198 moves ((U R2 Uv2 R' Uv' R Uv' U)6 Uv)52 5 checkerboard shifted twice ((U R2 Uv2 R' Uv' R Uv' U)6 Uv2')24 5 checkerboard shifted twice ((U2 R2 Uv2 R' Uv' R Uv')6 Uv2')24 5 checkerboard shifted twice, 576 moves ( (F2 R2' F2' U R' U2' F2 R2' F U2' F2 U' R2 U F2' U2 F2 R U' R2) Uv')32 5 checkerboard shifted twice, 640 moves CORNER/0p EDGE/2p CENTER/3p 40 (X Rv X Uv2 Fv2')8 (1:2 4:1 5:8 8:3) 40 751 (Fv2' ( U' L2 U2 BL2 L BL2' L U2' L U2 BL2 L2 BL2' L2 U') Rv Uv2' U L U2 L U2' BL2' U2 BL2 L BL2' U2' BL2 U2 L2' U2 Uv2' )8 Fv 5 checkerboard shifted twice, 240 moves (Fv2 Uv Fv' BLv Fv' L2' U2' F U' L2' F U F2 U2 F' U2 F2' L' U F2' U2 F2' L U2' L2' U' L' U BR2' U2 BR2 BL BR2' U2' BR2 U2 BL2' U2' BL U2 BL Uv2' Rv)6 Rv' 5 checkerboard shifted twice, 216 moves (Fv2 Uv Fv' BLv Fv' L2' U2' F U' L2' F U F2 U2 F' U2 F2' L' U F2' U2 F2' L U2' BL BR2' BL' L2' U' L' U BR2 U2 BR2' BL' U2' BL U2 BL BR2 Uv2' Rv)6 Rv' 5 checkerboard shifted twice, 210 moves ((U Fv2 D')90 Uv')20 (((2U 2L)12 Fv')24 Uv')5 2 stars, 10 tridents order 2 CORNER/0p EDGE/2p CENTER/3p 72 (X' Uv' X Fv X Rv' X' Fv Fv)8 (1:2 2:2 5:8 8:2) 40 751 ((U' BL' R' BR' U' BR U BL R U BR U' BR' U)' Uv' (U' BL' R' BR' U' BR U BL R U BR U' BR' U) Fv (U' BL' R' BR' U' BR U BL R U BR U' BR' U) Rv' (U' BL' R' BR' U' BR U BL R U BR U' BR' U)' Fv2)8 Fv close to 10 checkerboard, 448 moves ( U' R2' U2 F U R F' R2 F U' F' R' U R2' U2 R2 U BL' Uv' Fv ( BL' R' BR' U' BR U BL R U BR U' BR' U) Rv' U' BR U BR' U' R' BL' U' BR' U BR R BL U Fv2)8 Fv close to 10 checkerboard, 360 moves (BL U' R2' U2 F U R F' R2 F U' F' R' U R2' U2 R2 U' Uv' Fv (U2' R2' BR' R' E' BR U' BR' E2 BR2 U2 BR' E' BR' R' BF' BR') Rv' BR' U BR R BL U Fv2)8 Fv close to 10 checkerboard, 328 moves (twsearch improvement) CORNER/0p EDGE/2p CENTER/3p 90 (Fv Fv X' Uv' X' Uv' X' BLv X BLv)9 (1:4 5:8 9:2) 45 751 (Fv Fv (R F U F' U' R' L' U' F' U F L)' Uv' (R F U F' U' R' L' U' F' U F L)' Uv' (R F U F' U' R' L' U' F' U F L)' BLv (R F U F' U' R' L' U' F' U F L) BLv)9 close to 10 checkerboard type 2, 432 moves ((2U 2L)36 Rv2')12 10 checkerboard order 5, 864 slice moves ((2U 2L)24 Uv2)12 10 checkerboard order 5, 576 slice moves (Uv (U R')12 (C A')12 Fv')14 10 checkerboard order 5, 672 moves (U2 R2' U R' F2' U2' F2 U' R2' U F2' U2 F' R2 F2' U2 R U' F2 R2 F2' U2' Fv2 U2 R2' U R' F2' U2' F2 U' R2' U F2' U2 F' R2 F2' U2 R U' F2 R2 F2' U2' Fv2' Rv)14 10 checkerboard order 5, 616 moves ((U2 R2' U2' R2 F' U2' F R2' U2 R2' U2' R2 F' U2' F R2')' Fv' (U2 R2' U2' R2 F' U2' F R2' U2 R2' U2' R2 F' U2' F R2') Uv)14 10 checkerboard order 5, 448 moves (Fv F2' U2 F2 U2' F' U' F' U2 F U2 F' U' F' U2' F2 U2 F2' U2 Fv U' F2' U2' F2 U2 F' U F' U' F U' F' U F' U2 F2 U2' F2' U2 Rv2 F2' U2 F2 U2' F' U' F' U2 F U2 F' U' F' U2' F2 U2 F2' U2)8 10 checkerboard order 5, 440 moves (U2 L2' U2' L2' F' U2 L' F' L F' L2 F2 L2' F2' U F U2 L2 U2' L2' F2 L2 F2 U' BR2' R2 BR2 R2' BR' R' BR' R2 BR R2 BR' R' BR' R2' BR2 R2 BR2' R2 Rv2')8 10 checkerboard order 5, 336 moves ((U2' L2' U2 L2 F L2' U2' L2 U2 F2' U2' F U2 F) Rv F2' U F U2' F' U2' F U F2 U' F2 U2 F2' U2 F2 U' F' Fv2' Rv F2' U F U2' F' U2' F U F2 U' F2 U2 F2' U2 F2 U' F' Fv)9 10 checkerboard order 5, 432 moves (Fv F U2 F U2' F U2 F' U F2 U2 F2' U F2' U2 F2 U F' U2 F U2' L2 U2' L2 U L2 U' L U2' L' U L U2 L' U L2' U2' L2 U L2' U2 L2' U' Uv' Rv Fv' ( U' F U F2' U2' F U2' F2 U F U F U2 F U2' F2 U2' F' U2' F2' U F2'))6 10 checkerboard order 5, 384 moves (2U 2L 2U 2L 2U 2L 2U 2L 2U 2L 2U 2L 2U 2L 2U 2L 2U 2L 2U 2L 2U 2L 2U 2L Uv2)42 10 checkerboard order 5 (2U 2L 2U 2L 2U 2L 2U 2L 2U 2L 2U 2L 2U 2L 2U 2L 2U 2L 2U 2L 2U 2L 2U 2L Uv')24 10 checkerboard order 5 (2U 2L 2U 2L 2U 2L 2U 2L 2U 2L 2U 2L 2U 2L 2U 2L 2U 2L 2U 2L 2U 2L 2U 2L Rv2)24 10 checkerboard order 5 shifted twice CORNER/0p EDGE/2o CENTER/2p 96 (X' Rv' X Rv' X' Fv2')16 (1:2 2:1 4:2 5:6 8:1 16:2) 80 541 10 checkerboard order 5, 672 moves ((L U L2' U2' L2 BL2 L2' BL2' U BL2 L2 BL2' L2' U L) Rv' Uv (L U' L2' U' L2 BL2 L2' BL2' U' BL2 L2 BL2' L2' U2 L) Rv2' (L U' L2' U' L2 BL2 L2' BL2' U' BL2 L2 BL2' L2' U2 L) Fv' (L U L2' U2' L2 BL2 L2' BL2' U BL2 L2 BL2' L2' U L) Rv2')6 10 checkerboard order 5, 360 moves ((L U L2' U2' L2 BL2 L2' BL2' U BL2 L2 BL2' L2' U L) Rv' Uv (L U' L2' U' L2 BL2 L2' BL2' U' BL2 L2 BL2' L2' U2 L) Rv2' (R2' L U' R2' U' R' U' R2 U' R2 U2' R2 U2' R U2' R U R U2 R U2 L' Fv') Rv2')6 10 checkerboard order 5, 312 moves (U' BR' BL BR2 U2' BR2' BL BR2 U BL' U BL2 BR BL2 U2 BL2 U2' BR' U2' BR2' BL2' U' Rv' Uv Rv2' ( R2' L U' R2' U' R' U' R2 U' R2 U2' R2 U2' R U2' R U R U2 R U2 L' ) Fv' Rv2')6 10 checkerboard order 5, 264 moves ((U' BR' BL BR2 U2' BR2' BL BR2 U BL' U BL2 BR BL2 U2 BL2 U2' BR' U2' BR2' BL2' U') BRv' Lv2 (R2' L U' R2' U' R' U' R2 U' R2 U2' R2 U2' R U2' R U R U2 R U2 L' ) Fv' Rv2')6 10 checkerboard order 5, 264 moves, less rot CORNER/0p EDGE/2o CENTER/2p 48 (Fv Fv X Uv Rv' Rv' X Rv' Uv' Uv' X' Rv)4 (1:8 4:8 5:6) 20 541 (U2' BR' BL BR2 U2' BR2' BL BR2 U BL' U BL2 BR BL2 U2 BL2 U2' BR' U2' BR2' BL2' BRv' Lv2 BL2 BR2 U2 BR U2 BL2' U2' BL2' BR' BL2' U' BL U' BR2' BL' BR2 U2 BR2' BL' BR U2 Fv' Rv2')6 10 checkerboard order 5 (anticlockwise), 252 moves (Fv2 Uv2 ( F2 U F2 U F U F2' U F2' U2 F2' U2 F' U2 F' U' F' U2' F' U2') Rv Fv (U2 F U2 F U F U2' F U2' F2 U2' F2 U' F2 U' F' U' F2' U' F2') Uv2 Rv ( F2 U F2 U F U F2' U F2' U2 F2' U2 F' U2 F' U' F' U2' F' U2'))4 10 checkerboard order 5 (clockwise), 240 moves ( BL2 U' BL2' U BR2' R2' U' BL2' U BR2' R2' U' BR2 BL2 U R2 U' BR2 BL' U BL2' C2' D C2 D' A2 I2 D C2 D' A2 I2 D A2' C2' D' I2' D A2' C D' C2 BL2 U' BL2' U BR2' R2' U' BL2' U BR2' R2' U' BR2 BL2 U R2 U' BR2 BL' U BL2' C2' D C2 D' A2 I2 D C2 D' A2 I2 D A2' C2' D' I2' D A2' C D' C2 Uv2)2 10 checkerboard order 5, 168 moves (BR2 U' BR2' U R2' F2' U' BR2' U R2' F2' U' R2 BR2 U F2 U' R2 BR' U BR2' BLv2' Rv F2' U F2 U' R2 BR2 U F2 U' R2 BR2 U R2' F2' U' BR2' U R2' F U' F2 Lv2 BLv)2 10 checkerboard order 5, 84 moves ***BEST*** (Uv2' Rv (2R' 2BR2' 2R2' 2L 2BR')6 Uv' (2R' 2BR2' 2R2' 2L 2BR')6 Lv Uv (2R' 2BR2' 2R2' 2L 2BR')6 Uv Lv (2BR 2L' 2R2 2BR2 2R)6)2 10 checkerboard order 5 (240 slice moves) CORNER/0p EDGE/2o CENTER/2p 84 (X Rv2' X Rv2' X Uv')14 (1:4 5:6 14:2) 70 541 CORNER/0p EDGE/2o CENTER/2p 48 (Fv Uv Fv Uv Fv Uv Fv Uv Fv' X12 Uv' X36)4 (1:6 2:4 4:6 5:6) 20 541 CORNER/0p EDGE/2o CENTER/2p 96 (Fv Uv Fv Uv2 X Uv' X Rv2 X Rv2 Uv2' X)8 (1:2 2:1 4:1 5:6 8:4) 40 541 (Rv Fv2 F U F' U F2' U2 F' U2 F' U2 F' U2 F2' U' F2' U2 F' U F U F2 U2 Rv2 Fv (U2' F2' U' F' U' F U2' F2 U F2 U2' F U2' F U2' F U2' F2 U' F U' F'))8 10 checkerboard order 5 shifted twice, 352 moves CORNER/0p EDGE/2o CENTER/2p 42 (Uv' X4 Rv' Uv2' X4' Rv2')7 (1:4 5:6 7:4) 35 541 (Uv' (U2' F2' U' F' U F U F U F2 U2 F2 U2' F' U' F U' F' U' F' U' F2) Rv' Uv2' F2' U F U F U F' U F U2 F2' U2' F2' U' F' U' F' U' F U F2 U2 Rv2')7 10 checkerboard order 5 shifted twice, 308 moves (U2' F2' U' F' U F U F U F2 U2 F2 U2' F' U' F U' F' U' F' U' F2 BF2' BR BF BR BF BR BF' BR BF BR2 BF2' BR2' BF2' BR' BF' BR' BF' BR' BF BR BF2 BR2 Fv)7 10 checkerboard order 5 shifted twice, less rot, 308 moves ( BL2 U' BL2' U BR2' R2' U' BL2' U BR2' R2' U' BR2 BL2 U R2 U' BR2 BL' U BL2' C2' D C2 D' A2 I2 D C2 D' A2 I2 D A2' C2' D' I2' D A2' C D' C2 BL2 U' BL2' U BR2' R2' U' BL2' U BR2' R2' U' BR2 BL2 U R2 U' BR2 BL' U BL2' C2' D C2 D' A2 I2 D C2 D' A2 I2 D A2' C2' D' I2' D A2' C D' C2 Uv')3 10 checkerboard order 5 shifted twice, 252 moves ( BL2 U' BL2' U BR2' R2' U' BL2' U BR2' R2' U' BR2 BL2 U R2 U' BR2 BL' U BL2' C2' D C2 D' A2 I2 D C2 D' A2 I2 D A2' C2' D' I2' D A2' C D' C2 Uv)3 10 checkerboard order 5 shifted twice, 126 moves *** BEST *** ./twsearch.order -A2 --settarget 541 --mindepth 25 --setorder 5 --moves 2L,2U,Uv,Fv,Rv mm-slice-plus1.tws CORNER/0p EDGE/2o CENTER/2p 1200 (2U 2L 2U 2L 2U 2L 2U 2L 2U 2L 2U 2L 2U 2L 2U 2L 2U 2L 2U 2L 2U 2L 2U 2L Fv')48 (1:2 5:6 6:1 8:2 16:1) 240 541 10 checkerboard order 5 shifted twice ((Fv' 2U 2L)24)18 10 checkerboard order 5 shifted twice, 864 slice moves ((2L 2R')12 Uv2')24 10 checkerboard order 5 shifted twice, 576 slice moves ( U2' F2 U2' F2' U2 F U F U2' F' U2' F U F U2 F2' U2' F2 Rv2' F2' U2 F2 R2 U R2' U F2' U F2 R2 U2 R2' U2 Rv2 Fv')12 10 checkerboard order 5 shifted twice, 384 moves CORNER/0p EDGE/2o CENTER/2p 48 (Rv2 X)24 (1:2 2:5 5:6 8:2 12:1) 120 541 (Rv2 (2U 2L)12)24 10 checkerboard order 5 shifted twice, 576 slice moves (Rv2' (F' L' U')8 Rv2 (F' L' U')16 Uv2)9 10 checkerboard order 5 shifted twice, 648 moves CORNER/0p EDGE/2o CENTER/2p 45 (Uv2' X2 Rv2' X Rv2)9 (1:2 3:1 5:6 9:3) 45 541 10 checkerboard order 5 shifted twice, 648 moves X = (U L F)8 CORNER/0p EDGE/2o CENTER/2p 36 (X3' Rv2' Uv2' X3 Rv2 Fv2)6 (1:2 3:2 5:6 6:4) 30 541 10 checkerboard order 5 shifted twice, 864 moves (Fv2 Uv' (2U 2R 2F)28 Fv (2U 2R 2F)28)5 12 checkerboard order 2, 840 slice moves (Fv2' Uv' (2U 2L)24)15 12 checkerboard order 2, 720 slice moves CORNER/0p EDGE/2o CENTER/2p 45 (Fv2 X2' Uv)15 (2:16 15:2) 30 541 (Fv' Uv' (D' E' BF')8 (U L F)8 Rv' (D' E' BF' )8 (U L F)8)7 12 checkerboard order 2, 672 moves (Fv' Rv Rv Uv' (L2' I2 D2' E2 R2' U2)8 (U R')12 Rv (U2' R2 E2' D2 I2' L2)8)5 12 checkerboard order 2, 600 moves (Fv2 Uv (BR2 U' BR2' U R2' F2' U' BR2' U R2' F2' U' R2 BR2 U F2 U' R2 BR' U BR2') Rv Fv' (F2 U' F L2' U BL2' U' F2' L2' U BL2 L2 U' F2 U BL2 L2 U' F2 U F2') Rv' (BR2 U' BR2' U R2' F2' U' BR2' U R2' F2' U' R2 BR2 U F2 U' R2 BR' U BR2') Fv' Rv' (BR2 U' BR R2' U F2' U' BR2' R2' U F2 R2 U' BR2 U F2 R2 U' BR2 U BR2'))7 12 checkerboard order 2, 588 moves (Fv Uv' (C2' D E2' D2 C2 D2' C2' D C2 D C2' D' E2 D' C2 D2') (BL2 U' L2 U2 L2' U BL2' U L2 U' L2' U' L2 U2 L2' U2') Fv2 Rv2' (D2 C2' D E2' D C2 D' C2' D' C2 D2 C2' D2' E2 D' C2) (U2 L2 U2' L2' U L2 U L2' U' BL2 U' L2 U2' L2' U BL2'))7 12 checkerboard order 2, 448 moves (Fv2 Uv Fv (2L' 2U')12 Lv' Fv' (Lv E L' Uv D U')12 Rv' (2U 2L )12 Uv (U D' Uv' L E' Lv')12)3 12 checkerboard order 2 (Fv2 Lv F2 U2 F U2' R2' F U2 F2 R2 U' F2 U2' F2 R2' U2' F U' F2 R2 U2 R' U Rv2 F2' U2' F U' F2 U2' F2' U2 F2' U2 F2' U2' F2 U' F U2' F2' U2 )9 12 checkerboard order 2, 360 moves (Fv2 Uv2' F2' U R2' F2' U2' F' R2 U2 F' U2' F2' U' R U2' R2' F2' U F' U2 R2 F2' Rv' R2' F' R U2 R2' F2' U2 R2 U' R2 F2' U2 R2' F2' R2 F U2 F2' R2' U' R2' U2' R' U2 F2 R2 BLv' Uv' U' R U2' R2' F2' U F' U2 R2 F2' U2 F2' U R2' F2' U2' F' R2 U2 F' U2' F2')5 12 checkerboard order 2, 345 moves ( BL2 U' BL2' U BR2' R2' U' BL2' U BR2' R2' U' BR2 BL2 U R2 U' BR2 BL' U BL2' C2' D C2 D' A2 I2 D C2 D' A2 I2 D A2' C2' D' I2' D A2' C D' C2 Rv' BL2 U' BL2' U BR2' R2' U' BL2' U BR2' R2' U' BR2 BL2 U R2 U' BR2 BL' U BL2' C2' D C2 D' A2 I2 D C2 D' A2 I2 D A2' C2' D' I2' D A2' C D' C2 Uv2')3 12 checkerboard order 2, 252 moves, ***BEST*** ((2L' 2U')12 Rv' (2L' 2U' )12 Rv' Uv (2L' 2U')12 Fv')5 12 checkerboard order 2, 360 slice moves (Fv Uv (Rv2' 2L' 2U')12 Fv Rv' (2U 2L Rv2)12 Fv' Uv Rv (2U 2L Rv2)12 Fv(2U 2L Rv2)12)3 12 checkerboard order 2, 288 slice moves (Fv2 Uv Rv' Uv (2U 2L Rv2)12 BLv Uv2 (2U 2L)12 Fv'(Rv2' 2L' 2U')12 )3 12 checkerboard order 2, 216 slice moves X = F' L2' U' L' U L2' F2' U2' L2' F' L' F L F L2 F2' L2' F2 U2 F2' U2' Y = F2 U2 F U2 F2' U' F2' U F2 U' F2' U' F' U F U2 F U2' F2 CORNER/0p EDGE/2o CENTER/2p 90 (Fv Uv X Fv' X' Rv' Rv' X Fv Y)9 (+2:16 3:1 9:3) 18 541 CORNER/0p EDGE/2o CENTER/2p 80 (Fv2' Z Rv2 Y X)16 (3:12 4:2 16:2) 48 541 (Fv2' (U2' F2 U2' F2' U2 F U F U2' F' U2' F U F U2 F2' U2' F2) Rv2 (BL2 U BL2' L2' BL2 L2 U L2' BL2' L2 BL2 U2' BL2' U) (R F U F' U' R' L' U' F' U F L))16 12 checkerboard order 3, 704 moves (Fv Rv' Uv' (U2 BL' L F2')6 Fv' Rv' (U2 BL' L F2')6 Rv' Uv (U2 BL' L F2')6)8 12 checkerboard order 3, 576 moves ((U2' F2' U' F' U F U F U F2 U2 F2 U2' F' U' F U' F' U' F' U' C2' F' C' F C F C F C2 F2 C2 F2' C' F' C F' C' F' C' F' C2 BR2' U2' BR' U' BR U BR U BR U2 BR2 U2 BR2' U' BR' U BR' U' BR' U' BR' U2) Uv' Fv2)8 12 checkerboard order 3, 512 moves ((F2' U' F' U F U F U F2 U2 F2 U2' F' U' F U' F' U' F' U' C2' F' C' F C F C F C2 F2 C2 F2' C' F' C F' C' F' C' F' C2 BR2' U2' BR' U' BR U BR U BR U2 BR2 U2 BR2' U' BR' U BR' U' BR' U' BR' ) Uv' Fv2)8 12 checkerboard order 3, 496 moves (((2U 2L)12 Fv')24 Uv)10 12 checkerboard order 3, 5760 slice moves (Fv Rv (2U 2L)48)13 12 checkerboard order 3, 1248 slice moves CORNER/0p EDGE/2o CENTER/2p 39 (Fv Rv X4)13 (1:4 3:12 13:2) 39 541 ((2U 2L)12 Fv Rv)20 12 checkerboard order 3, 480 slice moves ((2U 2L)12 Fv Rv2')10 12 checkerboard order 3, 240 slice moves (Uv2' Fv (2U 2L)12)10 12 checkerboard order 3, 240 slice moves CORNER/0p EDGE/2o CENTER/2p 30 (Uv2' Fv X)10 (3:12 10:4) 30 541 ((U2' F2 U2' F2' U2 F U F U2' F' U2' F U F U2 F2' U2' F2) Fv2' Uv L' F' U' F U L R U F U' F' R' Rv2' U2' F2 U2 F' U F L2 F2 L2' F' U' F' U L2 F' L2' F2' U2 F2' U2' Fv)8 12 checkerboard order 3, 400 moves ((U2' F2 U2' F2' U2 F U F U2' F' U2' F U F U2 F2' U2' F) Fv2' Uv F' U' F U L R U F U' F' R' Rv2' U2' F2 U2 F' U F L2 F2 L2' F' U' F' U L2 F' L2' F2' U2 F2' U2' Fv)8 12 checkerboard order 3, 392 moves (Fv' Uv' (U F' U' F2 L U' F2' L U2' F2 U2 F2' U2 L' U2 F2 L' F' U) Rv' Uv2' Fv' U2 F2 U2' F2' L2 F2 L2' F' L' F' L F L2 U2 F2 L2 U' L U L2 F Rv')8 12 checkerboard order 3, 320 moves (( U F' U' F2 L U' F2' L U2' F2 U2 F2' U2 L' U2 F2 L' F' U BL2 BF2 BL2' BF2' BR2 BF2 BR2' BF' BR' BF' BR BF BR2 BL2 BF2 BR2 BL' BR BL BR2 BF) BLv2' Uv2)8 12 checkerboard order 3, 320 moves, simplified (Fv Uv' Rv Fv U2' R BL2' BR2' R' BL U2' R BR2' R' BL Uv' Fv' BL' R BR2 R' U2 BL' R BR2 BL2 R' U2 Fv' BL' R BR2 R' U2 BL' R BR2 BL2 R' U2)8 12 checkerboard order 3, 264 moves (Fv Uv' Rv Fv R2' U2' BL2' R BR2' BL R' U2' R BR2' BL Uv' Fv' R BR2 R' U2 BL' R BR2 BL2 R' U2 BR' Fv' R BR2 R' U2 BL' R BR2 BL2 R' U2)8 12 checkerboard order 3, 256 moves, ***BEST*** ((2L' 2U')12 Rv Fv' (2U 2L)12 Rv)5 12 checkerboard order 3, 240 slice moves ((U2 R2')12 Uv' Fv2' (U R')12 Fv' Uv Fv')10 CORNER/0p EDGE/2o CENTER/2p 80 (X Uv' Fv' Fv' Y Fv' Uv Fv')10 (2:3 3:12 10:3) 30 541 12 checkerboard order 3, 480 moves ((2U 2L)24 Fv2' Rv)35 6 checkerboard, 6 tridents order 3, 1680 slice moves ((2U 2L 2F)6 Fv)9 10 stars order 5, 162 slice moves (Fv2 Uv Fv2 Uv D U' E2' L2 D U' E2 L2' D U' E2' L2 D U' E2 L2' D U' E2' L2 D U' E2 L2' D U' E2' L2 D U' E2 L2' D U' E2' L2 D U' E2 L2' D U' E2' L2 D U' E2 L2' Rv D U' E2' L2 D U' E2 L2' D U' E2' L2 D U' E2 L2' D U' E2' L2 D U' E2 L2' D U' E2' L2 D U' E2 L2' D U' E2' L2 D U' E2 L2' D U' E2' L2 D U' E2 L2' Rv)2 10 stars order 5, 192 moves ((L2 E2' U2 D2' L2' E2 U2 D2')3 Uv2)7 10 stars order 5, 168 moves EDGE/0p CENTER/0p 14 (X' Fv')7 (1:8 5:8 7:2) 35 1110 ((2L 2F 2U)6' Fv')7 10 stars shifted twice order 5, 126 slice moves EDGE/0p CENTER/0p 36 (Fv Uv' X' Uv X' Uv Rv X Fv X Rv Rv)3 (1:10 3:4 5:8) 15 1110 (Fv Uv' (L' U')9 Uv (L' U')9 Uv Rv (U L)9 Fv (U L)9 Rv Rv)3 10 stars shifted twice order 5, 216 moves (Fv Uv' F2' L2 U2' L2' F U' F2' U' L2 U2 L' F2' U' L U2' L' U2' F2 L' U2 F' U' (F' U')4 F' U' Uv2 Rv U L (U L)7 U L2 Fv L (U L)8 Rv2)3 10 stars shifted twice order 5, 201 moves (Rv2 (L2 E2' U2 D2' L2' E2 U2 D2' L2 E2' U2 D2' L2' E2 U2 D2' L2 E2' U2 D2' L2' E2 U2 D2') Rv' Uv Fv Uv D2 E2' D2 E2 D2 E2' D2 E2 D2 E2' D2 E2 U2' L2 U2' L2' U2' L2 U2' L2' U2' L2 U2' L2' Fv Rv D2 E2' D2 E2 D2 E2' D2 E2 D2 E2' D2 E2 U2' L2 U2' L2' U2' L2 U2' L2' U2' L2 U2' L2' Fv)2 Lv 10 stars shifted twice order 5, 144 moves (Av2 Fv E L' D' U E L' D U' E L' D' U E L' D U' E L' D' U E L' D U' Fv2 Ev' (U D' L E' U' D L E' U D' L E' U' D L E' U D' L E' U' D L E'))2 10 stars shifted twice order 5, 96 moves (Av2 Fv E L' D' U E L' D U' E L' D' U E L' D U' E L' D' U E L' D2 U2' Fv2 Ev' ( L E' U' D L E' U D' L E' U' D L E' U D' L E' U' D L E'))2 10 stars shifted twice order 5, 92 moves EDGE/0p CENTER/0p 14 (Fv X Fv X Fv X Fv X Fv X Fv X Fv X)1 (1:22 5:8) 5 1110 (Fv (2L 2F 2U)6)7 10 stars shifted twice order 5, 126 slice moves EDGE/0p CENTER/0p 81 (Fv2 Uv X)27 (2:22 3:2 27:2) 54 1110 12 stars o2 (Rv2 (2U 2L 2F)6 Fv' Uv' (2U 2L 2F)6 Fv2')3 12 stars o2, 108 slice moves, 216 moves (Fv2 Uv Fv Uv' Fv E L' D' U E L' D U' E L' D' U E L' D U' E L' D' U E L' Uv2' (U D' L E' U' D L E' U D' L E' U' D L E' U D' L E' U' D L E') Uv (L E' U' D L E' U D' L E' U' D L E' U D' L E' U' D L E'))3 12 stars o2, 204 moves (D2' E D2 E' D E2 D2 E2' D E2' D2 E2 D E' D2 E D2' E Rv' Uv2' (E' D2 E' D2' E D' E2' D2' E2 D' E2 D2' E2' D' E D2' E' D2) Uv' Fv2')5 12 stars o2, 180 moves ***BEST*** (Fv Rv (2L 2F 2U)6)16 12 stars order 3, 288 slice moves (Fv' Uv' (2L 2F 2U)6)14 12 stars order 3, 252 slice moves ((2L 2F 2U)6 Rv (2U' 2F' 2L')12 Fv Rv2)4 12 stars order 3, 216 slice moves (Uv (2U' 2F' 2L')6 Rv (2L 2F 2U)6 Rv' Uv (2L 2F 2U)12 Fv')2 12 stars order 3, 144 slice moves, 288 moves (Fv (U L)9 Fv Rv' U' F U F U2' F2 L2' U2' F U2 F2' U2' F U2 F2' L2 U F U F2' Uv Fv2' (U L)9 Rv Uv')5 12 stars order 3, 280 moves (Fv2 Rv' R' U' F' U' R' F' U2' F' U R2' U2' R' F R2' U2' F R U F2' R U' F2 L2' U2' F U2 F2' U2' F U2 F2' L2 U F U F2' Uv Fv2' (U L)9 Rv Uv')5 12 stars order 3, 270 moves (Fv2 Uv2' (L2 E2' U D' L2' E2 U D' L2 E2' U D' L2' E2 U D' L2 E2' U D' L2' E2) Uv2 E2' L2 D U' E2 L2' D U' E2' L2 D U' E2 L2' D U' E2' L2 D U' E2 L2' Fv' Rv' (L2 E2' U D' L2' E2 U D' L2 E2' U D' L2' E2 U D' L2 E2' U D' L2' E2 U D') Uv')2 12 stars order 3, 136 moves ( (L2 E2' U D' L2' E2 U D' L2 E2' U D' L2' E2 U D' L2 E2' U D' L2' E2 I2' R2 ) Uv2 D U' E2 L2' D U' E2' L2 D U' E2 L2' D U' E2' L2 D U' E2 L2' Fv' Rv' (L2 E2' U D' L2' E2 U D' L2 E2' U D' L2' E2 U D' L2 E2' U D' L2' E2 U D') Lv2 Uv2)2 12 stars order 3, 136 moves, simplified ***BEST*** (Fv Fv Uv Fv' Uv Rv' U F R2 F U2 R2 F2 U2 R2 U2 F R' U2' F2' R2' U2' F2' U' F' U2 F U' R2' U2' R' F' Uv' U F R2 F U2 R2 F2 U2 R2 U2 F R' U2' F2' R2' U2' F2' U' F' U2 F U' R2' U2' R' F' Uv F2' L2 F L' F' L' F2 R U L U' R' L' Rv)5 30 flip (325 moves) (Fv Fv Uv' (F2' L2 F L' F' L' F2 R U L U' R' L') (U F R2 F U2 R2 F2 U2 R2 U2 F R' U2' F2' R2' U2' F2' U' F' U2 F U' R2' U2' R' F') Rv' (F2' L2 F L' F' L' F2 R U L U' R' L') Rv' Fv (F2' L2 F L' F' L' F2 R U L U' R' L') Rv' U F R2 F U2 R2 F2 U2 R2 U2 F R' U2' F2' R2' U2' F2' U' F' U2 F U' R2' U2' R' F')3 30 flip (273 moves) (Fv Fv U F R2 F U2 R2 F2 U2 R2 U2 F R' U2' F2' R2' U2' F2' U' F' U2 F U' R2' U2' R' F' Fv' Uv U F R2 F U2 R2 F2 U2 R2 U2 F R' U2' F2' R2' U2' F2' U' F' U2 F U' R2' U2' R' F' Uv F2' L2 F L' F' L' F2 R U L U' R' L' Rv Uv F2' L2 F L' F' L' F2 R U L U' R' L' Rv)3 30 flip (234 moves) (Fv Fv Uv Fv Rv Rv F2' L2 F L' F' L' F2 R U L U' R' L' Rv' F2' L2 F L' F' L' F2 R U L U' R' L' Rv' Rv' F2' L2 F L' F' L' F2 R U L U' R' L')5 30 flip (195 moves) (Fv Fv Uv Uv F' U2' F2 U F2 L' U' L U F2 U2' F' U2' L F L' Fv' Rv' F2' L2 F L' F' L' F2 R U L U' R' L' Uv F2' L2 F L' F' L' F2 R U L U' R' L' Rv' F' U2' F2 U F2 L' U' L U F2 U2' F' U2' L F L')3 30 flip (174 moves) (R2' F' U' F2 U R F' R U F U2' F' R' U R Rv' Rv' R2' F' U' F2 U R F' R U F U2' F' R' U R Uv Rv)5 30 flip (150 moves) (R2' F' U' F2 U R F' R U F U2' F' R' U R' Rv2' F' U' F2 U R F' R U F U2' F' R' U R Uv Rv)5 30 flip (145 moves, easy simplification) check 541 --------- (1:2 2:1 4:1 5:6 8:4) 10 check o5 (1:2 2:1 4:2 5:6 8:1 16:2) 10 check o5 (1:2 2:6 5:6 6:2 7:2) 10 check o5 (1:2 3:4 5:6 6:4) 10 check o5 (1:2 5:6 6:1 12:3) 10 check o5 ((2U 2L)24 Uv2)12 (1:4 2:2 5:6 12:2) 10 check o5 (1:4 5:6 14:2) 10 check o5 (1:6 2:4 4:6 5:6) 10 check o5 (1:8 4:8 5:6) 10 check o5 (1:32 5:6) 10 check o5 (1:4 4:1 5:6 12:3) 10 check o5 sh2 (1:2 5:6 6:3 18:1) 10 check o5 sh2 (1:2 5:6 6:1 8:2 16:1) 10 check o5 sh2 (1:8 4:3 5:6 8:3) 10 check o5 sh2 (1:4 5:6 7:4) 10 check o5 sh2 (1:2 3:2 5:6 6:4) 10 check o5 sh2 (1:2 2:3 5:6 6:4 12:1) (1:2 2:5 5:6 8:2 12:1) (1:2 4:1 5:6 12:1 14:2) (2:1 3:12 7:2 14:1) 12 check o3 (2:2 3:12 4:1 8:3) 12 check o3 (2:3 3:12 10:3) 12 check o3 (3:12 10:1 20:1) 12 check o3 (3:12 10:4) 12 check o3 (3:12 4:1 5:2 16:1) 12 check o3 (1:2 2:16 7:4) 12 check o2 (1:3 2:16 3:3 9:2) 12 check o2 (2:16 3:10) 12 check o2 (2:16 15:2) 12 check o2 (2:16 3:1 9:3) 12 check o2 (2:16 5:6) 12 check o2 541 order 2 can be 12 check o2 + 6 twist given any operation X that generates 10 checkerboard order 5 then (X Av' Uv2')3 generates 12 checkerboard order 2 edge pattern 130 ---------------- EDGE/1p CENTER/0p 1 (X)1 (1:56 3:2) 3 130 stars 1110 ---------- (1:22 5:8) 10 stars sh2 o5 (1:8 5:8 7:2) 10 stars sh2 o5 X = (U L)9 EDGE/0p CENTER/0p 72 (Fv Fv Uv Fv X Rv Uv' Rv X Rv' X Fv')6 (1:2 2:1 5:8 6:3) 30 1110 10 stars sh2 o5 EDGE/0p CENTER/0p 48 (Fv Fv X' Rv' Fv X Uv X' Uv' Rv X' Uv)4 (1:2 2:6 4:2 5:8) 20 1110 10 stars sh2 o5 (3:14 10:2) 12 stars o3 (2:22 3:8) 12 stars o2 (2:22 3:2 27:2) 12 stars o2 other interesting keys: 821 bowties 951 ----------- X = L' F R2 F2' L2' F2' U F L U' L' F L2 F2' R' F' R' F' L CORNER/0p EDGE/2p CENTER/4p 4 (Uv2 X)2 (1:4 2:4 5:10) 10 951 EDGE/0p CENTER/1o 1 (X)1 (1:52 5:2) 5 210 bowties shifted twice partial stars ------------- EDGE/0p CENTER/2o 1 (X)1 (1:42 5:4) 5 410 5 checkerboard 110 & 410 & 751 ------------------------------ X = 5 checkerboard EDGE/0p CENTER/2o 1 (X)1 (1:42 5:4) 5 410 X = 10 tridents EDGE/0p CENTER/2o 1 (X)1 (1:42 5:4) 5 410 X = (U R')12 CORNER/0p EDGE/2p CENTER/3p 24 (Uv2' X)12 (1:2 4:1 5:8 6:2 12:1) 60 751 CORNER/0p EDGE/2p CENTER/3p 24 (X Uv2' X Uv2' X Uv2' X Uv2')3 (1:4 3:6 5:8) 15 751 X = (F2 R2' F2' U R' U2' F2 R2' F U2' F2 U' R2 U F2' U2 F2 R U' R2 Uv2')12 EDGE/0p CENTER/0p 1 (X)1 (1:57 5:1) 5 110 halfway to 10 checker --------------------- EDGE/0p CENTER/1p 1 (X)1 (1:47 5:3) 5 310 3 cycle of edges ---------------- EDGE/3p 1 (X)1 (1:59 3:1) 3 70 5 interior edges plus top 5 edges --------------------------------- EDGE/0p CENTER/1o 1 (X)1 (1:52 5:2) 5 210 Part of bowties --------------- two 3 cycles of edges X = L' F R2 F2' L2' F2' U F L U' L' F L2 F2' R' F' R' F' L EDGE/1p CENTER/0p 1 (X)1 (1:56 3:2) 3 130 one fourth part of 10 checkerboard ---------------------------------- EDGE/4p CENTER/0p 1 (X)1 (1:53 3:3) 3 190 partial 10 stars ---------------- BR2' R2 BR' U BR R2' BR' U2' BR2' U' BR2 R2 U' R2' BR2' L2 BL2 R2 U2 BL2' L2' U2 R2' U' L2 BL2 U' BL2' U2 L2' BL2 U2' L2 U2' L2' F2 R2 U2' R2' F2' U2' BL2' R2 F2 U2' F2' U2' R2' F2 U2' F2' R2 U2' R2' U CORNER/0p EDGE/1p 1 (X)1 (1:47 5:3) 5 31