Pretty Patterns

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Order 3

Permutation
(+urf) (-dbl)
(ur,rf,fu) (bd,dl,lb) (ur1,fu1,rf1) (bd1,lb1,dl1) (ur2,fu2,rf2) (bd2,lb2,dl2)
(+r,f,u) (-l,-b,d) (r1,f1,u1,-r4,-f4,-u4,++r3,++f3,++u3,+r2,+f2,+u2) (l1,-b4,d1,+l2,b1,+d2,++l3,+b2,++d3,-l4,++b3,-d4) (r5,-u8,+f6,-r8,++u7,++f7) (u5,f5,++r7,+u6,-f8,+r6) (l5,d5,b5,-l8,-d8,+b6) (l6,d6,++b8,+l7,+d7,+b7)

2 Chessboard Cubes (4x4x4)

Algorithm Walter Randelshofer 2013
L' B MD2 B' D' B MD2 B' D L
R F' MD2 F U F' MD2 F · U' D2 · F2 L D · R2 L' · U' R U R2 U2 R' F D R' U
WR' MD' MR · MD2 WD' · NR NL' · NU' ND · CF' CD (44 btm, 57 ftm, 72 qtm)

Algorithm Per Kristen Fredlund 2014
MD MF · MD2 WD · NF NB' · ND' NU
R2 F2 WR B' MR2 B SR B' MR2 B U2 R2 D'
R2 L · B2 R' B' U2 WF' WR F' WD2 L D2 F' D2 F U2 (37 btm, 52 ftm, 70 qtm)

Algorithm André Boulouard 2014
MD MF · MD2 SD' · NL NR' · ND' NU
U2 L B' R2 F2 L' B D2 F2 L2 WF' R MF2 R' WF D MF2 D' L2 T4F2 R2 F2 U' SR' U' F2 R2 (35 btm, 48 ftm, 66 qtm)

Algorithm Walter Randelshofer 2018
D' WF' D' B' U' F' WD B2 · R L2 · B SD B' U' F2 R2
MR2 U SR U' MR2 U SR' B2 L2 MF
NU' ND · MF2 SF' · MR MF WR' (33 btm, 48 ftm, 60 qtm)

Algorithm Christopher Mowla 2018
U' L2 F D B R' B2 U F' SR' U WR2 B D' L' WD'
MF' U2 MF · D MD' · R2 MD B' D'
MD · NB NF' · MD2 SD' · MR MD (32 btm, 46 ftm, 54 qtm)

Algorithm Christopher Mowla 2018, Walter Randelshofer 2018
T4B' R F L2 B · U' D2 · WR' WD' L B2 D' L2 WF2 U' L'
MR2 B WR' U' MR2 U B2 L2
MD · NR NL' · MD2 WD · MR MD (31 btm, 44 ftm, 58 qtm)

Algorithm Christopher Mowla 2018, Walter Randelshofer 2018
L' F WR B' WD2 L F' R B2 U B' R D' L
MR2 F' WR' D' MR2 D' F2 R2
MD · NR NL' · MD2 WD · MR MD (29 btm, 41 ftm, 52 qtm)

Algorithm Christopher Mowla 2018, Walter Randelshofer 2018
R B' WR F WD2 R' B L' F2 D' F L' U R'
MR2 B WR' U MR2 U B2 L2
MD · NR NL' · MD2 WD · MR MD (29 btm, 41 ftm, 52 qtm)