| Move | Right | Up | Front | Left | Down | Back |
|---|---|---|---|---|---|---|
| ○● +90° | R |
U |
F |
L |
D |
B |
| ○● +180° | R2 |
U2 |
F2 |
L2 |
D2 |
B2 |
| ●● +90° | CR |
CU |
CF |
CL |
CD |
CB |
| ●● +180° | CR2 |
CU2 |
CF2 |
CL2 |
CD2 |
CB2 |
| Permutation | Right | Up | Front | Left | Down | Back |
| Faces | r |
u |
f |
l |
d |
b |
| Orientation | Plus: | + |
Minus | - |
||
| Cycle | Begin: | ( |
End: | ) |
||
| Delimiter | , |
|||||
| Syntax | precircumfix | |||||
| Grouping | ||||||
| Grouping | Begin: | ( |
End: | ) |
||
| Repetition | ||||||
| Syntax | suffix | |||||
| Inversion | ||||||
| Invertor | - |
|||||
| Syntax | suffix | |||||
| Delimiter | ||||||
| NOP | · . |
|||||
Randelshofer ENG 2x2 is a notation for Rubik's Pocket Cube. The notation is based on the English language. It supports 90° and 180° twists of the faces of the cube. The whole cube can be rotated along its face axes. Permutation and orientation changes of individual cube parts can be specified using permutation cycles. The notation supports the following high-level constructs: grouping, repetition, inversion.
Notation used to describe moves
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Clockwise 90° twists of the six faces are denoted by the capital letters: «R», «U», «F», «L», «D» and «B», (right, up, front, left, down, back).
Clockwise 90° rotations of the whole cube along the three face axes are denoted by the capital letter «C» followed by a face twist: «CR», «CU», «CF», «CL», «CD» and «CB».
180° twists and rotations are denoted by appending the number «2» to a move: «U2», «CU2», ... .
Counterclockwise twists and rotations are denoted by applying the inversion operator «-» to a move: «U-», «CU-», ... .
Notation used to describe permutation cycles
-----------------------------------------
A permutation cycle is described by a list of the affected cube parts. The list is enclosed in round brackets «(» «)». The cube parts in the list are separated by commas «,».
A cube part is described by the faces on which its stickers can be seen. The faces of the cube are denoted by the lower-case letters: «r», «u», «f», «l», «d» and «b», (right, up, front, left, down, back).
Example: A corner part having its stickers at the upper front right corner is denoted by the three letters: «ufr».
The face names in a permutation cycle are used to describe orientation changes of the parts. The first face name describes where the first sticker goes. The second face name describes where the second sticker goes, and so on.
Example: The move «R» is equivalent to the permutation cycle: «(urf,bru,drb,frd)»
If the last cube part in a cycle needs to be reoriented when it moves to the beginning of the cycle, a sign character is prepended to the first cube part in the cycle. The «+» sign denotes a clockwise orientation change. The «–» sign denotes a counterclockwise orientation change.
Example: The sequence of moves «R U» causes the cube parts to perform the permutation cycle «(-ufl,ulb,ubr,bdr,dfr) (+urf)».
High-level constructs
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High-level constructs can be applied to moves and to permutation cycles.
Logically distinct sequences of moves can be separated using a no operation marker: «·» (middle-dot) or «.» (dot). For example, if a long sequence of moves has been constructed of multiple short sequences (maneuvers).
Sequences of moves can be grouped using round brackets: «(R U F)».
Sequences of moves can be repeated multiple times by appending the number of repetitions to the closing bracket: «(R U F)3».
Sequences of moves can be inverted by appending the inversion operator «-» to the closing bracket: «(R U F)-».
High-level constructs can be nested: «(R U F)3-».
References
----------------------------
This notation is based on the notation for Rubik's Pocket Cube by Walter Randelshofer, as published at http://www.randelshofer.ch/rubik/pocket/notation/randelshofer_eng.html
Walter Randelshofer 2007