CubeTwister

Superset ENG 7x7

Move Right Up Front Left Down Back
○○○○○○● +90° R U F L D B
○○○○○○● +180° R2 U2 F2 L2 D2 B2
○○○○○●● +90° TR TU TF TL TD TB
○○○○○●● +180° TR2 TU2 TF2 TL2 TD2 TB2
○○○○●●● +90° T3R T3U T3F T3L T3D T3B
○○○○●●● +180° T3R2 T3U2 T3F2 T3L2 T3D2 T3B2
○○○●●●● +90° T4R T4U T4F T4L T4D T4B
○○○●●●● +180° T4R2 T4U2 T4F2 T4L2 T4D2 T4B2
○○●●●●● +90° T5R T5U T5F T5L T5D T5B
○○●●●●● +180° T5R2 T5U2 T5F2 T5L2 T5D2 T5B2
○●●●●●● +90° T6R T6U T6F T6L T6D T6B
○●●●●●● +180° T6R2 T6U2 T6F2 T6L2 T6D2 T6B2
●●●●●●● +90° CR CU CF CL CD CB
●●●●●●● +180° CR2 CU2 CF2 CL2 CD2 CB2
○○○○○●○ +90° NR NU NF NL ND NB
○○○○○●○ -90° N6L N6D N6B N6R N6U N6F
○○○○○●○ +180° NR2 NU2 NF2 NL2 ND2 NB2
○○○○○●○ -180° N6L2 N6D2 N6B2 N6R2 N6U2 N6F2
○○○○●○○ +90° N3R N3U N3F N3L N3D N3B
○○○○●○○ -90° N5L N5D N5B N5R N5U N5F
○○○○●○○ +180° N3R2 N3U2 N3F2 N3L2 N3D2 N3B2
○○○○●○○ -180° N5L2 N5D2 N5B2 N5R2 N5U2 N5F2
○○○●○○○ +90° MR N4R MU N4U MF N4F ML N4L MD N4D MB N4B
○○○●○○○ +180° MR2 N4R2 MU2 N4U2 MF2 N4F2 ML2 N4L2 MD2 N4D2 MB2 N4B2
○○○○●●○ +90° VR N2-3R VU N2-3U N5-6D' VF N2-3F VL N2-3L VD N2-3D VB N2-3B
○○○○●●○ -90° N5-6L N5-6D N5-6B N5-6R N5-6U N5-6F
○○○○●●○ +180° VR2 N2-3R2 VU2 N2-3U2 VF2 N2-3F2 VL2 N2-3L2 VD2 N2-3D2 VB2 N2-3B2
○○○○●●○ -180° N5-6L2 N5-6D2 N5-6B2 N5-6R2 N5-6U2 N5-6F2
○○○●●○○ +90° M2R N3-4R M2U N3-4U M2F N3-4F M2L N3-4L M2D N3-4D M2B N3-4B
○○○●●○○ -90° N4-5L N4-5D N4-5B N4-5R N4-5U N4-5F
○○○●●○○ +180° M2R2 N3-4R2 M2U2 N3-4U2 M2F2 N3-4F2 M2L2 N3-4L2 M2D2 N3-4D2 M2B2 N3-4B2
○○○●●○○ -180° N4-5L2 N4-5D2 N4-5B2 N4-5R2 N4-5U2 N4-5F2
○○○●●●○ +90° V3R N2-4R V3U N2-4U V3F N2-4F V3L N2-4L V3D N2-4D V3B N2-4B
○○○●●●○ -90° N4-6L N4-6D N4-6B N4-6R N4-6U N4-6F
○○○●●●○ +180° V3R2 N2-4R2 V3U2 N2-4U2 V3F2 N2-4F2 V3L2 N2-4L2 V3D2 N2-4D2 V3B2 N2-4B2
○○○●●●○ -180° N4-6L2 N4-6D2 N4-6B2 N4-6R2 N4-6U2 N4-6F2
○○●●●○○ +90° M3R N3-5R M3U N3-5U M3F N3-5F M3L N3-5L M3D N3-5D M3B N3-5B
○○●●●○○ +180° M3R2 N3-5R2 M3U2 N3-5U2 M3F2 N3-5F2 M3L2 N3-5L2 M3D2 N3-5D2 M3B2 N3-5B2
○○●●●●○ +90° M4R V4R N2-5R M4U V4U N2-5U M4F V4F N2-5F M4L V4L N2-5L M4D V4D N2-5D M4B V4B N2-5B
○○●●●●○ -90° N3-6L N3-6D N3-6B N3-6R N3-6U N3-6F
○○●●●●○ +180° M4R2 V4R2 N2-5R2 M4U2 V4U2 N2-5U2 M4F2 V4F2 N2-5F2 M4L2 V4L2 N2-5L2 M4D2 V4D2 N2-5D2 M4B2 V4B2 N2-5B2
○○●●●●○ -180° N3-6L2 N3-6D2 N3-6B2 N3-6R2 N3-6U2 N3-6F2
○●●●●●○ +90° WR M5R V5R N2-6R WU M5U V5U N2-6U WF M5F V5F N2-6F WL M5L V5L N2-6L WD M5D V5D N2-6D WB M5B V5B N2-6B
○●●●●●○ +180° WR2 M5R2 V5R2 N2-6R2 WU2 M5U2 V5U2 N2-6U2 WF2 M5F2 V5F2 N2-6F2 WL2 M5L2 V5L2 N2-6L2 WD2 M5D2 V5D2 N2-6D2 WB2 M5B2 V5B2 N2-6B2
●●●●●○● +90° S2-2R S2-2U S2-2F S2-2L S2-2D S2-2B
●●●●●○● -90° S6-6L S6-6D S6-6B S6-6R S6-6U S6-6F
●●●●●○● +180° S2-2R2 S2-2U2 S2-2F2 S2-2L2 S2-2D2 S2-2B2
●●●●●○● -180° S6-6L2 S6-6D2 S6-6B2 S6-6R2 S6-6U2 S6-6F2
●●●●○●● +90° S3-3R S3-3U S3-3F S3-3L S3-3D S3-3B
●●●●○●● -90° S5-5L S5-5D S5-5B S5-5R S5-5U S5-5F
●●●●○●● +180° S3-3R2 S3-3U2 S3-3F2 S3-3L2 S3-3D2 S3-3B2
●●●●○●● -180° S5-5L2 S5-5D2 S5-5B2 S5-5R2 S5-5U2 S5-5F2
●●●○●●● +90° S3R S3U S3F S3L S3D S3B
●●●○●●● +180° S3R2 S3U2 S3F2 S3L2 S3D2 S3B2
●●●●○○● +90° S2-3R S2-3U S2-3F S2-3L S2-3D S2-3B
●●●●○○● -90° S6-6L S6-6D S6-6B S6-6R S6-6U S6-6F
●●●●○○● +180° S2-3R2 S2-3U2 S2-3F2 S2-3L2 S2-3D2 S2-3B2
●●●●○○● -180° S6-6L2 S6-6D2 S6-6B2 S6-6R2 S6-6U2 S6-6F2
●●●○○●● +90° S3-4R S3-4U S3-4F S3-4L S3-4D S3-4B
●●●○○●● -90° S4-5L S4-5D S4-5B S4-5R S4-5U S4-5F
●●●○○●● +180° S3-4R2 S3-4U2 S3-4F2 S3-4L2 S3-4D2 S3-4B2
●●●○○●● -180° S4-5L2 S4-5D2 S4-5B2 S4-5R2 S4-5U2 S4-5F2
●●●○○○● +90° S2-4R S2-4U S2-4F S2-4L S3-4D S3-4B
●●●○○○● -90° S4-6L S4-6D S4-6B S4-6R S4-6U S4-6F
●●●○○○● +180° S2-4R2 S2-4U2 S2-4F2 S2-4L2 S2-4D2 S2-4B2
●●●○○○● -180° S4-6L2 S4-6D2 S4-6B2 S4-6R2 S4-6U2 S4-6F2
●●○○○●● +90° S2R S2U S2F S2L S2D S2B
●●○○○●● +180° S2R2 S2U2 S2F2 S2L2 S2D2 S2B2
●●○○○○● +90° S2-5R S2-5U S2-5F S2-5L S2-5D S2-5B
●●○○○○● -90° S3-6L S3-6D S3-6B S3-6R S3-6U S3-6F
●●○○○○● +180° S2-5R2 S2-5U2 S2-5F2 S2-5L2 S2-5D2 S2-5B2
●●○○○○● -180° S3-6L2 S3-6D2 S3-6B2 S3-6L2 S3-6U2 S3-6F2
●○○○○○● +90° SR SU SF SL SD SB
●○○○○○● +180° SR2 SU2 SF2 SL2 SD2 SB2
 
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
 
Reflection
Reflector *
Syntax suffix
 
Conjugation
Conjugation Begin: < End: >
Syntax prefix
 
Commutation
Commutation Begin: [ End: ]
Delimiter ,
Syntax precircumfix
 
Rotation
Rotation Begin: < End: >'
Syntax prefix
 
Delimiter
NOP · .
 
Comment
Multi-Line Begin: /* End: */
Single-Line Begin: //

Superset ENG 7x7 is a notation for Rubik's Cubes with 7 layers, such as the V-Cube 7. 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. 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,
- reflection,
- conjugation,
- commutation, and
- rotation,
- single-line and multiple-line comments.


Single moves
===========================

Face twists: R, R', R2
----------------------------------
Clockwise 90° twists of the six faces of the cube are described by the capital letters: «R», «U», «F», «L», «D» and «B», (right, up, front, left, down, back).

Counterclockwise twists and rotations are described by applying the inversion operator «'» to a move: «R'», «U'», «F'», … .

In environments, where the the «'» character can not be used, the character «-» can be used as the inversion operator.

180° twists and rotations are described by appending the number «2» to a move: «R2», «U2», «F2», … .


Cube rotations: CR, CR', CR2
----------------------------------
Rotations of the whole cube are described by prepending the letter «C» to a face twist.

For example, «CR» rotates the whole cube in clockwise direction as seen from the right face.


Tier twists: TR, T3R, T4R, T5R, T6R
--------------------------------------
Twists which go multiple layers deep (tier twists) are described by prepending the letter «T» to a face twist: «TR», «TU'», «TF2».

The depth of the tier can be specified by inserting a number after the letter «T». For example, «T3R» twists three layers deep in clockwise direction as seen from the right face.

If the dept is not explicitly specified, the value «2» is assumed: «TL», «TD'», «TB2».

To keep scripts short, «T1R» is never used, because it is equivalent to «R». «T2R» is never used, because it is equivalent to «TR».


Mid-layer twists: MR, M2R, M3R, M4R, M5R
----------------------------------------
Twists of the layers in the middle (mid-layer twists) are described by prepending the letter «M» to a face twist: «MR», «MU'», «MF2».

On cubes with an even amount of layers, the mid-layers are the ones closer to the face of the cube.

The number of layers twisted can be specified by inserting a number after the letter «M». For example, «M2R» twists two layers in the middle in clockwise direction as seen from the right face.

If the depth is not explicitly specified, the value «1» is assumed, for example «ML», «MD'», «MB2».

To keep scripts short, «M1R» is never used, because it is equivalent to «MR».


Slice twists: SR, S2R, S3R
----------------------------------
Twists of opposing faces (slice twists) are described by prepending the letter «S» to a face twist. For example, «SR» turns the right face and the opposing left face in clockwise direction as seen from the right face.

The depth of the slices can be specified by inserting a number after the letter «S», for example «S2R».

If the depth is not explicitly specified, the value «1» is assumed, for example «SL», «SD'», «SB2».

To keep scripts short, «S1R» is never used, because it is equivalent to «SR».


Wide-layer twists: WR
----------------------------------
Twists of all layers except the outer faces (wide-layer twists) can be described by prepending the letter «W» to a face twist: «WR», «WU'», «WF2».

«WR» is equal to «M5R» and twists four layers in the middle in clockwise direction as seen from the right face.


Numbered layer twists: NR, N3R, N4R, N5R, N6R
-------------------------------------
Twists of an individual layer of the cube (twist of the n-th layer) are described by prepending the letter «N» to a face twist. The number of the layer can be specified by inserting the number of the layer after the letter «N», for example «N4R», «N3U'», «N5F2».

Layers are numbered starting from the face described by the face twist towards the opposite face. The layer at the face of the cube has number «1», the next layer has number «2», and so on.

If the layer is not explicitly specified, the value «2» is assumed, for example «NL», «ND'», «NB2».

To keep scripts short, «N1R» is never used, because it is equivalent to «R». «N2R» is never used, because it is equivalent to «NR».


Verge twists: VR, V3R, V4R, V5R
----------------------------------
Tier twists without the cube face (verge twists) can be described by prepending the letter «V» to a face twist: «VR», «VU'», «VF2».

The depth of verge layers can be specified by inserting a number after the letter «V». For example, «V3R» twists the layers 2 through 4 in clockwise direction as seen from the right face.

If the depth is not explicitly specified, the value «2» is assumed: «VL», «VD'», «VB2».

To keep scripts short, «V1R» is never used, because it is equivalent to «NR». «V2R» is never used, because it is equivalent to «VR».


Numbered range twists: N2-3R, N2-4R, N3-5R, N3-6R, N4-5R, N5-6R
----------------------------------
Twists of a range of layers are described by prepending the letter «N» to a face twist, followed by the number of the first layer, a "-" character, and the number of the last layer.

«N2-4R» twists the layers 2 through 4 in clockwise direction as seen from the right face.

To keep scripts short, ranges which start with 1 or end with the last layer of the cube are written as tier twists, instead of «N1-3F2» we write «T3F2», instead of «N5-7F» we write «T3B'». Ranges of only one layer are written as N layer twists, instead of «N2-2D'» we write «N2D'».


Slice range twists: S2-3R, S2-4R, S3-5R, S3-6R, S4-5R, S5-6R
----------------------------------
Slice twists around an arbitrary range of layers are described by prepending the letter «S» to a face twist, followed by the number of the first layer, a "-" character, and the number of the last layer.

«S3-4R» performs a slice twists around the layers 3 through 4 in clockwise direction as seen from the right face.

To keep scripts short, slice range twists are only used, if there is no equivalent slice twist. For example, instead of «S2-5F2» we write «SF2».


Constructs
===========================

Sequences of moves
----------------------------------
Sequences of moves are specified by appending moves, for example «R2L2UD'F2B2UD'».

To improve readability, whitespace can be used to separate moves: «R2 L2 U D' F2 B2 U D'».

Sequences of moves can be separated using a middle dot character «·». In environments where this character is not available, the full stop character can be used «.». The following sequences are equivalent: «R2 L2 · U D' · F2 B2 · U D'» and «R2 L2 . U D' . F2 B2 . U D'».


Grouping
----------------------------------
Sequences of moves can be grouped using brackets: «(R U F)».


Repetition
----------------------------------
Moves and groups can be repeated multiple times by appending the number of repetitions to the closing bracket: «(R U F)3».


Inversion
----------------------------------
Moves and groups can be inverted by appending the invertor operator «'» to the closing bracket: «(R U F)'».


Reflection
----------------------------------
Moves and groups can be reflected using the reflector operator «*»


Conjugation
----------------------------------
Conjugations of type A B A' are described by enclosing the conjugator A with angle brackets and prepending it to the conjugee B: «<A>B».


Commutation
----------------------------------
Commutations of type A B A' B' are described by enclosing the commutator A and the commutee B with square brackets and delimiting A and B by a comma: «[A,B]».

Rotation
----------------------------------
Rotations of type A' B A are described by enclosing the rotator A with angle brackets and appending a invertor operator. The rotator is then prepended to rotatee B: «<A>' B».


Permutation cycles
----------------------------------
A permutation of the cube is described by a sequence of parenthesized lists for each cycle of the cube parts which 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 described 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 described by the three letter sequence: «ufr».
e. g. An edge part having its stickers at the front right corner is described by the two letter sequence: «fr».
e. g. A side part having its sticker at the right face of the cube is described by the letter: «r».

Each cycle contains a list of either corner parts, edge parts or side parts which 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 described 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 */».

Werner Randelshofer, Walter Randelshofer 2008-08-17