| Move | Right | Up | Front | Left | Down | Back |
|---|---|---|---|---|---|---|
| ○○● +90° | R |
U |
F |
L |
D |
B |
| ○○● -90° | |
|
|
|
|
|
| ○○● +180° | R2 |
U2 |
F2 |
L2 |
D2 |
B2 |
| ○○● -180° | |
|
|
|
|
|
| ○●● +90° | |
|
|
|
|
|
| ○●● -90° | |
|
|
|
|
|
| ○●● +180° | |
|
|
|
|
|
| ○●● -180° | |
|
|
|
|
|
| ●●● +90° | CR |
CU |
CF |
CL |
CD |
CB |
| ●●● +180° | CR2 |
CU2 |
CF2 |
CL2 |
CD2 |
CB2 |
| ○●○ +90° | MR |
MU |
MF |
ML |
MD |
MB |
| ○●○ +180° | MR2 |
MU2 |
MF2 |
ML2 |
MD2 |
MB2 |
| ●○● +90° | |
|
|
|
|
|
| ●○● +180° | |
|
|
|
|
|
| Permutation | Right | Up | Front | Left | Down | Back |
| Faces | r |
u |
f |
l |
d |
b |
| Orientation | Plus: | + |
Minus | - |
||
| Plus Plus: | ++ |
|||||
| Cycle | Begin: | ( |
End: | ) |
||
| Delimiter | , |
|||||
| Syntax | precircumfix | |||||
| Grouping | ||||||
| Grouping | Begin: | ( |
End: | ) |
||
| Repetition | ||||||
| Syntax | suffix | |||||
| Inversion | ||||||
| Invertor | ' |
|||||
| Syntax | suffix | |||||
| Delimiter | ||||||
| NOP | · . |
|||||
| Comment | ||||||
| Multi-Line | Begin: | /* |
End: | */ |
||
| Single-Line | Begin: | // |
||||
| Macro | Script | Description |
|---|---|---|
CFU CUF CDB CBD |
CR CU2 |
|
CUB CBU CFD CDF |
CL CU2 |
|
CRU CUR CLD CDL |
CR2 CB |
|
CUL CLU CRD CDR |
CR2 CF |
|
CRF CFR CLB CBL |
CR2 CU |
|
CLF CFL CBR CRB |
CR2 CD |
|
CUFL CFLU CLUF CDBR CBRD CRDB |
CL CF |
|
CURF CRVU CFUR CDLB CLBD CBDL |
CR CU |
|
CRUB CUBR CBRU CLDF CDFL CFLD |
CR CB |
|
CBUL CULB CLBU CFDR CDRF CRFD |
CL CU |
|
CLFO CULF CFUL CRBD CDRB CBDR |
CR CD |
|
CFRU CUFR CRUF CBLD CDBL CLDB |
CL CB |
|
CBUR CRBU CURB CFDL CLFD CDLF |
CL CD |
|
CLUB CBLU CUBL CRDF CFRD CDFR |
CR CF |
Bandelow ENG is a notation for Rubik's Cube. The notation is based on the English language. It supports 90° and 180° twists of the faces of the cube. A whole cube can be rotated along its face axes, edge axes and corner 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.
Source:
Bandelow, Christoph. (1982). Inside Rubik's Cube and Beyond.
Birkhäuser Verlag, Boston.
Notation used for sequences of moves
----------------------------------
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° twists of the three middle layers are denoted by prepending the capital letter «M» (middle layer) to the face twists: «MR», «MU», «MF», «ML», «MD» and «MB».
Clockwise 90° rotations of the whole cube over the three face centered axes of the cube are denoted by prepending the capital letter «C» (cube rotation) to the face twists: «CR», «CU», «CF», «CL», «CD» and «CB».
Rotations of the whole cube over the six axes through the midpoints of antipodal edges are denoted by listing two faces and prepending the capital letter «C»: «CFU», «CUB», «CRU», ... .
Rotations of the whole cube over the four axes through antipodal corners are denoted by listing two faces and prepending the capital letter «C»: «CUFL», «CURF», «CRUB», ... .
180° twists and rotations are denoted by appending the number «2» to a move: «U2», «MU2», «CU2», ... .
Counterclockwise twists and rotations are denoted by applying the inversion operator «'» to a move: «U'», «MU'», «CU'», ... .
Sequences of moves can be grouped using 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 invertor operator «'» to the closing bracket: «(R U F)'».
Repition counts and inversions can be combined: «(R U F)3'» or «(R U F)'3».
Moves can be delimited using a no operation marker: «·» (middle-dot) or «.» (dot).
Notation used for permutations of cube parts
-----------------------------------------
A permutation of the cube is described by a sequence of parenthesized lists for each cycle of the cube parts that are permuted.
The location of a cube part is described by the faces on which its stickers can be seen. A face of the cubes is denoted by the lower-case letters: «r», «u», «f», «l», «d» and «b», (right, up, front, left, down, back).
e. g. A corner part having its stickers at the upper front right corner is denoted by the three letter sequence: «ufr».
e. g. An edge part having its stickers at the front right corner is denoted by the two letter sequence: «fr».
e. g. A side part having its sticker at the right face of the cube is denoted by the letter: «r».
Each cycle contains a list of either corner parts, edge parts or side parts that have been permuted.
The face names in a cycle are used to describe orientation changes of the parts. The first face name in a location description denotes where the first sticker goes. The second face name in a location description denotes where the second
sticker goes, and so on.
e.g. «(ufl,rfu)» describes, that the first sticker on face «u» at corner location «uf» goes to face «r» at corner location «rfu», the second sticker on face «f» at corner location «ufl» goes to face «f» at «rfu», and the third sticker on «l» at «ufl» goes to «u» at «rfu».
If the cube parts change orientation after going through a single cycle, then a prefix is added to the first location description of a sequence to denote this change in orientation.
If an edge part is flipped, a «+» prefix is added. If a corner part is twisted clockwise a «+» prefix is added, and if it is twisted counterclockwise a «–» prefix is added. If a side part is twisted 90° clockwise a «+» prefix is added, if it is twisted by 180° a «++» prefix is added and if it is twisted 90° counterclockwise a «-» prefix is added.
e. g. the move R is denoted by the following permutation: «(urf,bru,drb,frd) (ur,br,dr,fr) (+r)»
Comments
---------
Single line comments start with two slash characters: «// this is a comment».
Multiline comments starts with a slash and a star characer and end with star and a slash character: «/* this is a comment */».
Christoph Bandelow 1982