PocketCubeNotations

Superset ENG 2x2

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
 
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: //
Macro Script Description
CFU CUF CDB CBD CR CU2 Cube rotation along the edges fu-db
CUB CBU CFD CDF CL CU2 Cube rotation along the edges ub-fd
CRU CUR CLD CDL CR2 CB Cube rotation along the edges ru-ld
CUL CLU CRD CDR CR2 CF Cube rotation along the edges ul-rd
CRF CFR CLB CBL CR2 CU Cube rotation along the edges rf-lb
CLF CFL CBR CRB CR2 CD Cube rotation along the edge axis lf-br
CUFL CFLU CLUF CDBR CBRD CRDB CL CF Cube rotation along the corners ufl-dbr
CURF CRVU CFUR CDLB CLBD CBDL CR CU Cube rotation along the corners urf-dlb
CRUB CUBR CBRU CLDF CDFL CFLD CR CB Cube rotation along the corners rub-ldf
CBUL CULB CLBU CFDR CDRF CRFD CL CU Cube rotation along the corners bul-fdr
CLFO CULF CFUL CRBD CDRB CBDR CR CD Cube rotation along the corners lfo-rbd
CFRU CUFR CRUF CBLD CDBL CLDB CL CB Cube rotation along the corners fru-bld
CBUR CRBU CURB CFDL CLFD CDLF CL CD Cube rotation along the corners bur-fdl
CLUB CBLU CUBL CRDF CFRD CDFR CR CF Cube rotation along the corners lub-rdf

Superset 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, 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, reflection, conjugation, commutation, and rotation. Comments can be embedded into scripts.

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».

Rotations of the whole cube along the six edge axes are denoted by the capital leter «C» followed by two face twists: «CFU», «CUB», «CRU», ... .

Rotations of the whole cube along the four corner axes are denoted by the the capital letter «C» followed by three face twists: «CUFL», «CURF», «CRUB», ... .

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
----------------------------------
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)'».

Sequences of moves can be reflected by appending the reflection operator «*».

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

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

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

High-level constructs can be nested: «(R U F)3'» or «(R U F)'*».


Comments
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Multi-line comments are enclosed in «/*» and «*/»: «/* this is a comment */».

Single-line comments start with «//» : «// this is a comment».

Werner Randelshofer 2007