- Left and right edges in
*D*-layer together with the three adjacent centres - Left and right edges in
*B*-layer (together with the centre between them) - All four corners in
*D*-layer - Positioning
*U*-layer corners (PLLC) - Orienting
*U*-layer corners (OLLC) - Four remaining edges in
*R*and*L*layers, left/right pairwise - Orienting
*M*-layer edges (OMLE) - Positioning
*M*-layer edges (PMLE)

*U*,*D*,*F*,*B*,*R*and*L*layers: Up, Down, Front, Back, Right and Left*U*,*D*,*F*,*B*,*R*,*L*turns: clockwise turns of the corresponding layers- Composition
*T W*means: apply*T*first, then*W* *T . W*as a composition with a rhetoric pause in the middle*T2*:=*T T**T'*as the inverse of*T*, e.g. (*T W*)' =*W' T'*- Conjugator <
*T*>*W*:=*T W T'* - Commutator [
*T*,*W*] :=*T W T' W'* - E.g., (<
*T*>*W*)' = <*T*>*W'*and [*T*,*W*]' = [*W*,*T*] *R*,*M'*and*L'*represent parallel turns of the Right layer, vertical Middle slice and the Left layer- Together, they rotate the whole cube Front-to-Up
- I'd rather like if
*M*and*M'*slice turns were defined in the mutually opposite directions (consistent to*R*-layer turns), but...

- A good chance to find the first edge already aligned with the first centre
- 24 possibilities: 6 centres and 4 adjacent edges
- Align the second edge with its (second) adjacent centre
- Join them with the first center and edge
- There were two directions to go, take care about the corresponding colours
- Both edges can be usually solved in two or three side turns together
- Worst case, like SuperFlip, requires five turns

- Two choices: opt between
*U*or*D*layer for easier front and back edges (turn the cube upside-down if necessary) - Few cases with look-ahead and parallel solving are demonstrated by Java simulations

- Two choices: opt between solving corners in the layer with the first two edges solved, or with the second two edges solved
- You may solve the two corners common for both layers, then opt for two easier remaining corners
- Grab the cube by left (right) hand over the solved equator edges
- Use your right (left) hand exclusively for
*U*,*D*and*R*(*L*) turns - Insert corner by corner from
*D*layer to*U*layer, it's really ergonomic (and fast) *U*turns are needed here to avoid previously solved equator edges

- Two corners can be always aligned just by
*U*rotations - Two cases will remain: two adjacent and two diagonal swaps:
- Swapping two adjacent corners: [
*F'*,*U'*] (<*R*>*U*) =*F' U' F U R U R'* - Repeat/combine for diagonal corners
- Diagonal corners directly:
*F' U' R' F R F* - Symmetric left-handed algs:
*F U F' U' L' U' L*and*F U L F' L' F'*

- By Conservation laws, sum of the remaining corner twists must be zero
- Seven cases will remain upon the appropriate
*U*-layer prep turns: three positive twists, three negative, etc.: - Sune™ alg for three positive twists:
*T*:= <*R U*> [*R'*,*U*] =*R U R' U R U2 R'* - AntiSune™ alg for three negative twists:
*T'*= <*F U*> [*U*,*R'*] =*R U2 R' U' R U' R'* - Repeat/combine for the remaining five cases
- Symmetric left-handed algs:
*L' U' L U' L' U2 L*and*L' U2 L U L' U L* - Direct algs for remaining five cases:
- <
*F2 U2*>*F*=*F2 U2 F U2 F2* *F U2 F2 U' F2 U F2 U2 F'**F2 U' F U2 F' U2 F U' F2**W*:=*F2 R2 D R D' R F' U F'**W'*=*F U' F R' D R' D' R2 F2*- Symmetric left-handed algs:
*F2 U2 F' U2 F2*,*F' U2 F2 U F2 U' F2 U2 F*,*F2 U F' U2 F U2 F' U F2*,*F2 L2 D' L' D L' F U' F*and*F' U F' L D' L D L2 F2* - Observe how certain algs preserve additional F2L edges and try to save on the prep
*U*turns - Apply an one-time
*U*-layer alignment to complete the corners

- Useful trick:
- Consider
*a*and*b*as the left and right edges to be solved (or vice versa) - Insert the flipped edge
*a*to the destination of the edge*b* - Repeat the maneuver to insert now the edge
*b*(correctly flipped) to its proper destination - Edge
*b*will eject and roll over the edge*a*to its own destination

- By Conservation laws, sum of the edge flips must be even (none, two or four flips)
- Three cases will remain upon the appropriate cube or
*M*-slice prep turns: two adjacent flips, two diagonal and four flips: - Two adjacent flips:
*T*:= [*F2*, <*U*>*M'*] =*F2 U M' U' F2 U M U'* - Two diagonal flips:
*T'*= [<*U*>*M'*,*F2*] =*U M' U' F2 U M U' F2* - Repeat/combine for four flips
- Four flips directly:
*F M' F2 U2 F M2 F M' F2 U2 F*

- By Conservation laws, number of swaps (remaining swapped pairs of edges) must be even (none or two swaps)
- Four cases will remain upon the appropriate cube or
*M*-slice prep turns: anticlockwise and clockwise 3-cycles, two adjacent and two diagonal swaps: - Two overlapping swaps form 3-cycles:
- Anticlockwise:
*T*:= <*F2*>*M*=*F2 M F2* - Clockwise:
*T'*or <*U2*>*M'*=*U2 M' U2* - Repeat/combine for non-overlapping swaps
- Direct algs for non-overlapping swaps:
- Two adjacent swaps: <
*F2*>*M2*=*F2 M2 F2* - Two diagonal swaps: (<
*F2*>*M2*)(<*U2*>*M2*) =*F2 M2 F2 U2 M2 U2*

- Moving the OLLC step before PLLC gains no further optimizations for OLLC
- If OLLC is moved before PLLC, previous iF2L optimizations in PLLC will be lost
- Moving the PMLE step before OMLE cannot gain further optimizations for the already short PMLE algs

Illustrated by Java animated AnimCube by courtesy of J. Jelinek