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The 3x3x3 puzzle cube, or Rubik's Cube, is a puzzle toy consisting of a cube with each axis cut into three layers. In the solved state, the cube shows nine stickers of a matching color on each face. Twisting a layer moves the stickers around, mixing them up.
Each state of the puzzle is shown using ASCII rendering. All the renderings show the puzzle from at least two different angles. The UFR corner (up, front and right faces) of the puzzle are always visible in the first rendering, but the second rendering may show either the DFR corner or the DBL corner. Letters next to each face will indicate which corner is being shown.
A solved cube, showing the UFR and DBL corners, is shown here:
____________ B
U /_Y_/_Y_/_Y_/| +---+---+---+
/_Y_/_Y_/_Y_/B| | R | R | R |\
/ Y / Y / Y /B/| +---+---+---+G\
+---+---+---+B/B| R | R | R | R |\G\
| O | O | O |/B/| +---+---+---+G\G|
+---+---+---+B/B| | R | R | R |\G\|
| O | O | O |/B/ +---+---+---+G\G| L
+---+---+---+B/ \_W_\_W_\_W_\G\|
| O | O | O |/ \_W_\_W_\_W_\G|
+---+---+---+ D \_W_\_W_\_W_\|
F
The example cubes use the colors red (R), orange (O), yellow (Y), green (G), blue (B) and white (W). The following color net (arrangement of colors on the cube) is assumed:
Y GOBR W
The actual color scheme on your Rubik's Cube might vary. Japanese cubes, for example, often swap yellow and blue.
When reading algorithms (such as U R U' B'), the letter R will always refer to the right face (never the red face), and the letter B will always refer to the back face (never the blue face).
Ostensibly, cutting each axis of a cube into three layers will create 27 "cubies", or smaller cubes. If each outer face of the large cube is colored before cutting, 8 of the 27 cubies will have three colored faces (the "corners"), 12 wll have two colored faces (the "edges"), 6 will have one colored face (the "centers"), and 1 will have no colored faces (the "core").
In a plysical Rubik's Cube, the core is a 6-armed spindle to which the centers are attached by screws. This allows the remaining 20 cubies--the 12 edges and 8 corners--to move around without falling out.
12 Edges 8 Corners 6 Centers,
____ ____ ____ 1 Spindle
____/_Y_/____ / Y /| / Y /| ____
/_Y_/L__/_Y_/B|_ _+==-+ |_+==-+B| /_Y_/|
| / Y /| |/|B| / Y /||// Y /||/ _ |___|/+ _
L_+---+ L___/_|/ +---+ |++---+B|+_ //| | | /|//|
/ | O |/ /|/| | O |/ || O |/ /| ||===/_/==||B|
+---+---+---+B/B| +-==+=-++-==+=-+B| ||/+=--+| ||/
| O |/ | O |/|/ / /||// /||/ ++ | O ||
+---+---+--=L_/ +---+ |++---+B|+ +--++/_
| O |/ | O |/ | O |/ |___|/
+---+ +---+ +---+
We will denote each face of Rubik's Cube as follows:
Each face can be turned one of three ways. These are denoted as follows:
Shown below is the result of applying the move U:
____________ B
U /_Y_/_Y_/_Y_/| +---+---+---+
/_Y_/_Y_/_Y_/R| | G | G | G |\
/ Y / Y / Y /R/| +---+---+---+O\
+---+---+---+R/B| R | R | R | R |\O\
| B | B | B |/B/| +---+---+---+G\O|
+---+---+---+B/B| | R | R | R |\G\|
| O | O | O |/B/ +---+---+---+G\G| L
+---+---+---+B/ \_W_\_W_\_W_\G\|
| O | O | O |/ \_W_\_W_\_W_\G|
+---+---+---+ D \_W_\_W_\_W_\|
F
In algorithms (lists of moves to perform), uppercase letters and lowercase letters denote different types of moves. A lowercase letter denotes a double-layer move: the move r indicates to turn the R face 90 degrees clockwise, and to turn the layer between the L and R faces in the same direction.
Shown below is the result of applying r':
____________ B
U /_Y_/_R_/_R_/| +---+---+---+
/_Y_/_R_/_R_/B| | W | W | R |\
/ Y / R / R /B/| +---+---+---+G\
+---+---+---+B/B| R | W | W | R |\G\
| O | Y | Y |/B/| +---+---+---+G\G|
+---+---+---+B/B| | W | W | R |\G\|
| O | Y | Y |/B/ +---+---+---+G\G| L
+---+---+---+B/ \_O_\_O_\_W_\G\|
| O | Y | Y |/ \_O_\_O_\_W_\G|
+---+---+---+ D \_O_\_O_\_W_\|
F
To denote rotating the entire puzzle in your hands, the following notation is used:
These moves also have turn variations, such as x' or z2. They are always written in lowercase.
Some algorithms involve slice moves: turning the middle layer of a given axis while keeping the outer layers stationary. These are denoted thus:
These moves also have turn variations, such as M' and S2. They are always written in uppercase.
Shown below is the result of applying S2:
____________ B
U /_Y_/_Y_/_Y_/| +---+---+---+
/_W_/_W_/_W_/B| | R | R | R |\
/ Y / Y / Y /G/| +---+---+---+G\
+---+---+---+B/B| R | R | R | R |\B\
| O | O | O |/G/| +---+---+---+G\G|
+---+---+---+B/B| | R | R | R |\B\|
| O | O | O |/G/ +---+---+---+G\G| L
+---+---+---+B/ \_W_\_W_\_W_\B\|
| O | O | O |/ \_Y_\_Y_\_Y_\G|
+---+---+---+ D \_W_\_W_\_W_\|
F
An example algorithm, which solves the cube from the given starting position, reads as follows:
____________ B
U /_Y_/_Y_/_Y_/| +---+---+---+
/_O_/_Y_/_B_/O| | B | R | B |\
/ Y / Y / Y /Y/| +---+---+---+R\
+---+---+---+O/O| R | B | B | B |\Y\
| G | G | G |/O/| +---+---+---+R\R|
+---+---+---+O/O| | B | B | B |\R\|
| G | G | G |/O/ +---+---+---+R\R| L
+---+---+---+O/ \_W_\_W_\_W_\R\|
| G | G | G |/ \_W_\_W_\_W_\R|
+---+---+---+ D \_W_\_W_\_W_\|
F
y R U R' U' M U R U' r'
This means to do the following moves:
Note that slice notation and rotate notation can be converted back and forth. Some examples of equivalent algorithms include:
In my examples, sometimes the faces of cubies will be blank (no color will be indicated on them). Blank cubies can safely be ignored. A cube with all-blank cubies (except centers), showing the UFR and DFR corners, is shown here:
____________ F
U /___/___/___/| +---+---+---+
/___/_Y_/___/ | | | | |\
/ / / / /| +---+---+---+ \
+---+---+---+ / | R | | O | |\ \
| | | |/B/| +---+---+---+ \ |
+---+---+---+ / | | | | |\B\|
| | O | |/ / +---+---+---+ \ | R
+---+---+---+ / \___\___\___\ \|
| | | |/ \___\_W_\___\ |
+---+---+---+ D \___\___\___\|
F
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[Last updated: 2023-04-20]