1. orientation of last layer

1.1. awkward shapes ('y' shapes)

  • oll 29 (a1) sexy (R U' R') (F' U' F) (R U R') (solid y tipped right, pair in left f)
  • oll 30 (a2) F U (R U2 R' U') (R U2 R' U') F' (solid y upside down, pair in r)
  • oll 41 (a3) (R U R' U R U2' R') F sexy F' (dotted y with pair in bottom l)
  • oll 42 (a4) (R' U' R U' R' U2 R) F sexy F' (dotted y with pair in upper l)

1.2. knight move shapes (big l's)

  • solid l's are always in the f face
  • dotted l's have their bottoms in the r face
  • oll 13 (k1) (r U' r') (U' r U r') (F' U F) (solids pointing right)
  • oll 14 (k2) (R' F R) (U R' F' R) (F U' F') (solids pointing left)
  • oll 15 (k3) (r' U' r) inverse sexy (r' U r) (dots down)

  • oll 16 (k4) (r U r') sexy (r U' r') (dots up)

    (L tipped left, pair in lower left f face)

1.3. dots

  • oll 1 (o1) (R U2') long-sledge U2' sledge (single dot with vertical bars)
  • oll 2 (o2) F sexy F' f sexy f' (bar on left, two in B top and F bottom)
  • oll 3 (o3) f sexy f' U' F sexy F' (corner dot with dot in bottom)
  • oll 4 (o4) f sexy f' U F sexy F' (corner dot with dot in top)
  • oll 17 (o5) (R U R' U) sledge U2' sledge (slash with pairs in left and top)
  • oll 18 (o6) R U2' long-sledge U2' M' (U R U' r') (three dots with solid left bar)
  • oll 19 (o7) M U sexy M' sledge (three dots with pairs in left and right)
  • oll 20 (o8) M U sexy M2' (U R U' r') (full checkerboard)

1.4. i-shapes

  • oll 51 (i1) f sexy sexy f' (horizontal bar with dot pairs)
  • oll 52 (i2) R U R' U R d' R U' R' F' (vertical bar with solid bar on right)
  • oll 55 (i3) R U2 R2 U' R U' R' U2 F R F' (all vertical bars)
  • oll 56 (i4) r' U' r (U' R' U R) (U' R' U R) r' U r (horizontal bar with dots)

1.5. lightning bolts ('z' and 's' shapes)

  • oll 7 (b1) (r U R' U R U2' r') (left bolt with two pairs, dot in top)
  • oll 8 (b2) (r' U' R U' R' U2 r) (left bolt with two pairs, dot in bottom)
  • oll 11 (b3) M sune U M' (bottom s bolt with one pair in top)
  • oll 12 (b4) M' (R' U' R) (U' R' U2 R) U' M (top z bolt with one pair in bottom)
  • oll 39 (b5) (L F') left-sexy F U' L' (full z with pair in top left)
  • oll 40 (b6) (R' F) sexy F' U R (full z with pair in top right)

1.6. c shapes

  • oll 34 (c1) (R U R2' U') (R' F R U) R U' F' (c downwards with dots)
  • oll 46 (c2) R' U' sledge U R (full bar on right)

1.7. l-shapes (little l's)

all of these have the l on the right side, excluding l2

  • oll 47 (l1) F' left-sexy left-sexy F (dotted, l on top with pair in bottom left)
  • oll 48 (l2) F sexy sexy F' (dotted, l on top left with pair in bottom right)
  • oll 49 (l3) r U' r2' U r2 U r2' U' r (solid, l on top with pair in bottom)
  • oll 50 (l4) r' U r2 U' r2' U' r2 U r' (solid, l on bottom with pair in top)
  • oll 53 (l5) (r' U' R U') (R' U R U') R' U2 r (solid, l on bottom with headlights)
  • oll 54 (l6) (r U R' U) (R U' R' U) R U2' r' (solid, l on top with headlights)

1.8. w shapes

  • oll 36 (w1) (L' U' L) (U' L' U L) U (L F' L' F) (m on right, pair in front l face)
  • oll 38 (w2) (R U R') (U R U' R') U' sledge (m on left, pair in bottom of r face)

1.9. fish shapes

  • oll 9 (f1) sexy R' F (R2 U R' U') F' (partial fish, tail bottom right, two in left F)
  • oll 10 (f2) (R U R' U) sledge (R U2' R') (partial fish, tail top right, two in left B)
  • oll 35 (f3) (R U2') long-sledge (R U2' R') (solid fish, tail top left, dots)
  • oll 37 (f4) F (R U' R' U') (R U R' F') (soolid fish, tail bottom right)

1.10. squares

  • oll 5 (s1) r' U2' R U R' U r (bottom right square with matching l face)
  • oll 6 (s2) r U2 R' U' R U' r' (top right square with matching l face)

1.11. t shapes

  • oll 33 (t1) (R U R' U') (R' F R F') (solid t)
  • oll 45 (t2) F (R U R' U') F' (dotted t)

1.12. corners correct, edges flipped

  • oll 28 (e1) (r U R' U') M (U R U' R') (f and r edges)
  • oll 57 (e2) (R U R' U') M' (U R U' r') (f and b edges (h))

1.13. p-shapes

  • oll 31 (p1) S' (L' U' L U) (L F' L') f (b with dots on right)
  • oll 32 (p2) S (R U R' U') (R' F R f') (d on right with dots)
  • oll 43 (p3) f' (L' U' L U) f (b with bar on right)
  • oll 44 (p4) f (R U R' U') f' (d with bar on left)

1.14. all edges oriented correctly

  • oll 21 (ocll1) (R U R' U) (R U' R' U) (R U2' R') (dotted plus)
  • oll 22 (ocll2) R U2' R2' U' R2 U' R2' U2' R (plus with headlights)
  • oll 23 (ocll3) R2 D (R' U2 R) D' (R' U2 R') (headlights)
  • oll 24 (ocll4) (r U R' U') (r' F R F') (almost headlights)
  • oll 25 (ocll5) F' (r U R' U') r' F R (weird shape)
  • oll 26 (ocll6) R U2 R' U' R U' R' (sune)
  • oll 27 (ocll7) R U R' U R U2' R' (anti-sune)

2. permutation of last layer

2.1. one set of diagonal corners

  • v: (R' U R') d' (R' F' R2 U') (R' U R' F) R F
  • y: F (R U' R' U') (R U R' F') sexy sledge
  • na (R U R' U) (R U R' F') sexy (R' F R2 U') R' U2 (R U' R') (bottom right)
  • nb (R' U R U') (R' F' U' F) (R U R' F) R' F' (R U' R) (bottom left)

2.2. g permutations

  • ga R2 U (R' U R' U') (R U' R2) D U' (R' U R D') (bottom right in f)
  • gb (R' U' R U) D' (R2 U R') (U R U' R) U' R2 D (top right in r)
  • gc R2 U' (R U' R U) (R' U R2 D') unsexy D' (top right in b)
  • gd D' sexy D (R2 U' R U') (R' U R' U) R2 (bottom right in r)

2.3. corners only

  • aa l' U R' D2 R U' R' D2 R2 (headlights in back)
  • ab l' R' D2 R U R' D2 R U' R (headlights on right)
  • e x' (R U' R' D) (R U R' D') (R U R' D) (R U' R' D') x

2.4. edges only

  • ub (L' U L') (U' L' U' L') U L U L2 (opposite on left)
  • ua (R U' R) (U R U R) U' R' U' R2 (opposite on right)
  • z (M2' U M2' U) (M' U2) (M2' U2 M') [U2] (pair in right and front)
  • h (M2' U M2') U2 (M2' U M2') (checkerboard)

2.5. one set of adjacent corners

  • ra (R U' R' U') (R U R D) (R' U' R D') (R' U2 R') (pair in front)
  • rb (R' U2 R U2') R' F sexy R' F' R2 U' (pair in left)
  • ja (R' U L' U2) (R U' R' U2 R) L (bottom)
  • jb (R U R' F') sexy R' F R2 U' R' (left)
  • t sexy (R' F R2 U') R' U' (R U R' F') (pairs in back and front)
  • f (R' U' F') sexy (R' F R2 U') (R' U' R U) (R' U R) (solid bar on left)