| Move | Right | Up | Front | Left | Down | Back |
|---|---|---|---|---|---|---|
| ○○● +90° | R |
O |
V |
L |
U |
H |
| ○○● -90° | |
|
|
|
|
|
| ○○● +180° | R2 |
O2 |
V2 |
L2 |
U2 |
H2 |
| ○○● -180° | |
|
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|
|
| ○●● +90° | |
|
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|
| ○●● -90° | |
|
|
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|
| ○●● +180° | |
|
|
|
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|
| ○●● -180° | |
|
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|
|
| ●●● +90° | BR |
BO |
BV |
BL |
BU |
BH |
| ●●● +180° | BR2 |
BO2 |
BV2 |
BL2 |
BU2 |
BH2 |
| ○●○ +90° | MR |
MO |
MV |
ML |
MU |
MH |
| ○●○ +180° | MR2 |
MO2 |
MV2 |
ML2 |
MU2 |
MH2 |
| ●○● +90° | |
|
|
|
|
|
| ●○● +180° | |
|
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| Permutation | Right | Up | Front | Left | Down | Back |
| Faces | r |
o |
v |
l |
u |
h |
| Orientation | Plus: | + |
Minus | - |
||
| Plus Plus: | ++ |
|||||
| Cycle | Begin: | ( |
End: | ) |
||
| Delimiter | , |
|||||
| Syntax | precircumfix | |||||
| Grouping | ||||||
| Grouping | Begin: | ( |
End: | ) |
||
| Repetition | ||||||
| Syntax | suffix | |||||
| Inversion | ||||||
| Invertor | ' |
|||||
| Syntax | suffix | |||||
| Delimiter | ||||||
| NOP | · . |
|||||
| Macro | Script | Description |
|---|---|---|
BOV BVO BUH BHU |
BR BO2 |
|
BOH BHO BUV BVU |
BL BO2 |
|
BOR BRO BUL BLU |
BR2 BH |
|
BOL BLO BUR BRU |
BR2 BV |
|
BRV BVR BLH BHL |
BR2 BO |
|
BLV BVL BRH BHR |
BR2 BU |
|
BOVL BVLO BLOV BUHR BHRU BRUH |
BL BV |
|
BLVO BOLV BVOL BRHU BURH BHUR |
BR BU |
|
BORV BRVO BVOR BULH BLHU BHUL |
BR BO |
|
BVRO BOVR BROV BHLU BUHL BLUH |
BL BH |
|
BROH BOHR BHRO BLUV BUVL BVLU |
BR BH |
|
BHOR BRHO BORH BVUL BLVU BULV |
BL BU |
|
BHOL BOLH BLHO BVUR BURV BRVU |
BL BO |
|
BLOH BHLO BOHL BRUV BVRU BUVR |
BR BV |
Bandelow ENG is a notation for Rubik's Cube. The notation is based on the German 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. (1981). Einführung in die Cubologie.
Friedr. Vieweg & Sohn, Braunschweig/Wiesbaden.
Notation used for sequences of moves
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Clockwise 90° twists of the six faces are denoted by the capital letters: «R», «O», «V», «L», «U» and «H», (right "Rechts", up "Oben", front "Vorne", left "Links", down "Unten", back "Hinten").
Clockwise 90° twists of the three middle layers are denoted by prepending the capital letter «M» "Mittelschicht" to the face twists: «MR», «MO», «MV», «ML», «MU» and «MH».
Clockwise 90° rotations of the whole cube over the three face centered axes of the cube are denoted by prepending the capital letter «B» "Bewegung" to the face twists: «BR», «BO», «BV», «BL», «BU» and «BH».
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 «B»: «BVO», «BOH», «BRO», ... .
Rotations of the whole cube over the four axes through antipodal corners are denoted by listing two faces and prepending the capital letter «B»: «BOVL», «BORV», «BROH», ... .
180° twists and rotations are denoted by appending the number 2 to a move: «O2», «MO2», «BO2», ... .
Counterclockwise twists and rotations are denoted by applying the inversion operator «'» to a move: «O'», «MO'», «CO'», ... .
Sequences of moves can be grouped using brackets: «(R O V)».
Sequences of moves can be repeated multiple times by appending the number of repetitions to the closing bracket: «(R O V)3».
Sequences of moves can be inverted by appending the invertor operator «'» to the closing bracket: «(R O V)'».
Repition counts and inversions can be combined: «(R O V)3'» or «(R O V)'3».
Moves can be delimited using a no operation marker: «·» "middle dot" or «.» "point".
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.
Each cycle is enclosed into brackets: «(» and «)».
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», «o», «v», «l», «u» and «h», (right "rechts", up "oben",
front "vorne", left "links", down "unten", back "hinten").
e. g. A corner part having its stickers at the upper front right corner is denoted by the three letter sequence: «ovr».
e. g. An edge part having its stickers at the front right corner is denoted by the two letter sequence: «vr».
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. «(ovl,rvo)» describes, that the first sticker on face «o» at corner location «ovl» goes to face «r» at corner location «rvo», the second sticker on face «v» at corner location «ovl» goes to face «v» at «rvo», and the third sticker on «l» at «ovl» goes to «o» at «rvo».
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: «(orv,hro,urh,vru) (or,hr,ur,vr) (+r)»
Christoph Bandelow 1981