Editing Rubik's Cube (section)

===Singmaster notation===
Many 3×3×3 Rubik's Cube enthusiasts use a notation developed by [[David Singmaster]] to denote a sequence of moves, referred to as "Singmaster notation" or simple "Cube notation".<ref name="advgroup">{{Cite book |last=Joyner |first=David |url=https://archive.org/details/adventuresingrou0000joyn/page/7 |title=Adventures in group theory: Rubik's Cube, Merlin's machine, and Other Mathematical Toys |publisher=Johns Hopkins University Press |year=2002 |isbn=0-8018-6947-1 |location=Baltimore |page=[https://archive.org/details/adventuresingrou0000joyn/page/7 7]}}</ref> Its relative nature allows algorithms to be written in such a way that they can be applied regardless of which side is designated the top or how the colours are organised on a particular cube.
* ''F'' (Front): the side currently facing the solver
* ''B'' (Back): the side opposite the front
* ''U'' (Up): the side above or on top of the front side
* ''D'' (Down): the side opposite the top, underneath the Cube
* ''L'' (Left): the side directly to the left of the front
* ''R'' (Right): the side directly to the right of the front
* ''f'' (Front two layers): the side facing the solver and the corresponding middle layer
* ''b'' (Back two layers): the side opposite the front and the corresponding middle layer
* ''u'' (Up two layers): the top side and the corresponding middle layer
* ''d'' (Down two layers): the bottom layer and the corresponding middle layer
* ''l'' (Left two layers): the side to the left of the front and the corresponding middle layer
* ''r'' (Right two layers): the side to the right of the front and the corresponding middle layer
* ''x'' (rotate): rotate the entire Cube on ''R''
* ''y'' (rotate): rotate the entire Cube on ''U''
* ''z'' (rotate): rotate the entire Cube on ''F''

When a [[Prime (symbol)|prime symbol]] (&nbsp;′&nbsp;) follows a letter, it indicates an anticlockwise face turn; while a letter without a prime symbol denotes a clockwise turn. These directions are as one is looking at the specified face.  A letter followed by a&nbsp;2 (occasionally a superscript&nbsp;<sup>2</sup>) denotes two turns, or a 180-degree turn. For example, ''R'' means to turn the right side clockwise, but ''R′'' means to turn the right side anticlockwise. The letters ''x'', ''y'', and ''z'' are used to indicate that the entire Cube should be turned about one of its axes, corresponding to R, U, and F turns respectively. When ''x'', ''y'', or ''z'' is primed, it is an indication that the cube must be rotated in the opposite direction. When ''x'', ''y'', or ''z'' is squared, the cube must be rotated 180 degrees. <!-- Which axis (x, y, z) is which? user Nikevich -->

One of the most common deviations from Singmaster notation, and in fact the current official standard, is to use "w", for "wide", instead of lowercase letters to represent moves of two layers; thus, a move of ''Rw'' is equivalent to one of ''r''.<ref name="wcarules">{{Cite web |title=World Cube Association Competition Regulations |url=http://worldcubeassociation.org/regulations/ |access-date=5 May 2012 |publisher=World Cube Association}}</ref>

For methods using middle-layer turns (particularly corners-first methods), there is a generally accepted "MES" extension to the notation where letters ''M'', ''E'', and ''S'' denote middle layer turns. It was used e.g. in Marc Waterman's Algorithm.<ref>{{Cite book |last1=Treep |first1=Anneke |title=Marc Waterman's Algorithm, Part 2 |last2=Waterman |first2=Marc |publisher=Nederlandse Kubus Club |year=1987 |series=Cubism For Fun 15 |page=10}}</ref>
* ''M'' (Middle): the layer between L and R, turn direction as L (top-down)
* ''E'' (Equator): the layer between U and D, turn direction as D (left-right)
* ''S'' (Standing): the layer between F and B, turn direction as F

The 4×4×4 and larger cubes use an extended notation to refer to the additional middle layers. Generally speaking, uppercase letters (''F B U D L R'') refer to the outermost portions of the cube (called faces). Lowercase letters (''f b u d l r'') refer to the inner portions of the cube (called slices). An asterisk (L*), a number in front of it (2L), or two layers in parentheses (Ll), means to turn the two layers at the same time (both the inner and the outer left faces) For example: (''Rr'')<nowiki>'</nowiki>&nbsp;''l''2&nbsp;''f''<nowiki>'</nowiki> means to turn the two rightmost layers anticlockwise, then the left inner layer twice, and then the inner front layer anticlockwise. By extension, for cubes of 6×6×6 and larger, moves of three layers are notated by the number 3, for example, 3L.

An alternative notation, Wolstenholme notation,<ref>{{Cite web |title=Rubik's Cube - Solution and Wolstenholme Notation |url=http://www.topaccolades.com/notation/rubikscube.htm |access-date=19 February 2022 |website=topaccolades.com}}</ref> is designed to make memorising sequences of moves easier for novices.  This notation uses the same letters for faces except it replaces U with T (top), so that all are consonants.  The key difference is the use of the vowels O, A, and I for cl'''o'''ckwise, '''a'''nticlockwise, and tw'''i'''ce (180-degree) turns, which results in word-like sequences such as LOTA RATO LATA ROTI (equivalent to LU′ R′ U L′ U′ R U2 in Singmaster notation). The addition of a C implies rotation of the entire cube, so ROC is the clockwise rotation of the cube around its right face. Middle layer moves are denoted by adding an M to the corresponding face move, so RIM means a 180-degree turn of the middle layer adjacent to the R face.

Another notation appeared in the 1981 book ''[[The Simple Solution to Rubik's Cube]]''. Singmaster notation was not widely known at the time of publication. The faces were named Top (T), Bottom (B), Left (L), Right (R), Front (F), and Posterior (P), with + for clockwise, – for anticlockwise, and 2 for 180-degree turns.

Another notation appeared in the 1982 "The Ideal Solution" book for Rubik's Revenge. Horizontal planes were noted as tables, with table 1 or T1 starting at the top. Vertical front to back planes were noted as books, with book 1 or B1 starting from the left. Vertical left to right planes were noted as windows, with window 1 or W1 starting at the front. Using the front face as a reference view, table moves were left or right, book moves were up or down, and window moves were clockwise or anticlockwise.