Rubik’s Cube

Via Cedric Beust, circa 2003. Aims to be easy to memorize (few small moves).

Cube handling notes:

The cube has three pairs of opposite faces: Up/Down, Front/Back, Left/Right. Reorient as needed.
Move syntax uses one letter to reference a side, and optional direction marker. For example, U rotates the Up face clockwise, U' rotates anticlockwise.

Quick reference, final layer (w/minor personal tweaks):

1. FUR U'R'F' rotate front + right
1. URUR' URUUR' swap front + right
1. ULU'R' UL'U'R swap corners anticlockwise, except back left
1. RF'R'F RF'R'F rotate front right, only manipulate top between corners

The solve, first few steps left as an exercise to the reader:

Pick a colour to start, this is Up.
Solve Up edges.
Solve 3 Up corners.
Solve 3 middle edges, using the remaining Up corner as a “working” column.
Solve last Up corner.
Flip the cube, original Up colour is now Down.
Finish middle layer. Align last cube to match front colour and then: Move Up front to right front URU'R' U'F'UF Move Up front to left front U'L'UL UFU'F'
Orient Up edges. Flip front + right: FUR U'R'F' Flip front + back: FRU R'U'F'
Position Up edges. Rotate Up to try and match two, then, Swap left + back: UR'UUR UR'UR
Position Up corners. Sequence leaves back left untouched. Swap front left -> front right -> back right: ULU'R' UL'U'R
Orient Up corners. Keep the cube positioned with a consistent side as front, repeat sequence until oriented and then rotate Up layer only to bring a different corner to front-right. Parity will fix the rest of the cube when you’re done. Rotate front right: RF'R'F RF'R'F

Chinese Cube Instructions

- Solve Down edges, corners
- Middle layer edges: align edge to match Front or Right
  - Up Front to Front Right: FUFUFU'F'U'F'
  - Up Right to Front Right: R'U'R'U'R'URUR
  - Flip Front Right: RU2R' U RU2R' U F'U'F
- Up Cross
  - Flip Up Front & Up Back: FRUR'U'F'
  - Flip Up Front & Up Right: FURU'R'F'
- Up Face
  - Rotate 3 CCW, lock Up Back Left: R'U'RU'R'U2R
  - Rotate 3 CW, lock Up Front Left: RUR'URU2R' 
- Swap Up Corners
  - "Headlights" right face to front face: R2F2R'B'RF2R'BR'
  - "Headlights" front face to right face: RB'RF2R'BRF2R2
- Swap Up Edges
  - Lock Up Back, swap CCW: RU'RURURU'R'U'R2
  - Lock Up Back, swap CW: L'UL'U'L'U'L'ULUL2

TBD: Use this to generate some diagrams, and format this a bit more robustly.

Heise Method

No “algorithms” per se, focuses on building an intuitive feeling on how the cube works.

Make four 2x2 squares
Match squares and orient edges
Solve remaining edges and any 2 corners
Solve last 3 corners

8355 Method

Beginner method with few algorithms. Referenced several times is “Sexy move” RUR'U'.

Cross on Down
3 Down corners
- Position target corner in U above its desired location in D, and repeat sexy move until placed and oriented.
3 E-slice edges, using Keyhole method
- Position a target edge piece such that its Up color matches the Front face
  - Position keyhole under the desired location
  - Keyhole up/away from target, rotate Up to place target on the keyhole, return keyhole down.
  - This is either RU'R' if keyhole is to the right, or L'UL if keyhole is to the left.
Remaining edges
- Keep keyhole in front-right
  - Rotate Up to aim keyhole edge correctly relative to other correct Up edges
  - Rotate F' or R into place, rotate U to position another incorrect edge in that position, and restore keyhole with F or R'
  - To swap the last two edges, position the gap for the final Up edge as expected based on its orientation in the keyhole, and then either FR/UF: UF'UFU'FUF, or FR/UR: U'RU'R'U'RU'R'. (Intuitively, you’re moving the gap to last spot, and then bubbling the edges back and forth to fit them all in place.)
Final 5 corners
- Flip cube Up/Down
- If the keyhole corner UFR belongs in Down, rotate D until it is above its correct position, and repeat sexy move until placed and oriented. This will break the top of the cube, but only temporarily - just keep the orientation correct.
  - Rotate D to place next corner, and repeat.
  - When only 2 corners remain unplaced, repeat sexy move until the rest of the cube fixes itself, then rotate cube so unsolved corners are on Down layer.
  - Using a solved corner as the keyhole, repeat above to solve the cube:
    - if corners need to swap, sexy once to move corner up, rotate Down to the other corner, and sexy until placed, then rotate Down back and sexy until complete.
      - if corners just need to rotate, sexy to rotate the first, then rotate Down and sexy the other one til correct, and rotate Down back to complete.

Speed Cubing Method

https://lar5.com/cube/

Build 2x2x2 corner
Expand to 2x2x3
Orient unsolved faces as U and R
Fix “bad” edges, who orient “wrong” on to the two unsolved faces (whichever color they share)
- Correct FR and UL with F'U'F
Finish 2 layers, only turning the unsolved faces
- a. one corner + two edges
- b. final corner + edge
Orient cube so unsolved face is U
Position corners
- “Niklas” swaps UFR and UBR: LU'R'UL'U'RU2
- Swapping two diagonally opposite corners uses two Niklas.
Twist corners
- “Sune” selects a front corner, targeting its sticker on the front face, and rotates the other three corners.
  - UFR: BUB'UBU2B'U2
  - UFL: BU'B'U'BU2B'U2
- If 0 correct corners, target any U sticker
- If 1 correct corner, target the correct corner on the face with no U stickers
- If 2 correct corners, target non-U sticker of a twisted corner
Position edges
- Inspect top layer outer faces.
- If one edge is correct, orient it to B, and perform “Allan”: F2U' LR' F2 L'R U'F2 - This rotates counter-clockwise UL -> UF -> UR, to rotate clockwise change the U' turns to U.
- To swap two pairs of adjacent edges (F,R and L,B), “Bert”: F2B2 DR2 F2B2 L2 F2B2 D' F2B2
- To swap two pairs of opposite edges, “Arne”: R2F2B2L2 D L2B2F2R2