Talk:Rubik's Cube group

message: I've been extensively revising the Rubik's Cube group page for the last month or so. I think I'm more or less done with the first 3 sections and I'm getting ready to attack the 4th section.
Basically, if the Rubik's Cube is going to be mentioned by the Group article, a Featured Article, it should be a good understandable example. I'm aiming for WP:GA status. When the 4th section is understandable this article should be there.
Any help/reviews are appreciated.--Olsonist (talk) 23:03, 5 April 2012 (UTC)
thread_title: Major Revision

message: This article is extremely confusing. It throws around such terms as "legal", "fixed", and "orientation" without explaining or even defining them. Melchoir 03:48, 13 May 2006 (UTC)
thread_title: Confusing

message: I do not understand the first sentence
In mathematics, the Rubik's Cube is an interesting object because it provides a tangible representation of a mathematical group. 
Should'nt one say
In mathematics, the Rubik's Cube group is an interesting object because it both 
* gives insight into the mathematics behind the popular Rubik's Cube mechanical puzzle and
* provides a tangible representation of a mathematical group. 
--193.175.8.13 16:36, 26 October 2006 (UTC)
thread_title:  First sentence 

message: Center pieces should factor into the number of permutations because they do indeed move in 90 degree orientations. This may not be significant on normally colored cubes, however, not all cubes are normally colored. For instance, this becomes significant on a cube printed with a picture.  —Preceding unsigned comment added by 12.19.153.33 (talk) 13:11, 3 October 2008 (UTC)
replies: text: What do you mean by "flipping" a corner? Rotating a corner cube certainly does give a different element of the group, as the three facets on that corner cube will be interchanged. (Well, in fact rotation of a single corner cube is not in G at all; but a matching rotation of two corners is). –Henning Makholm 13:19, 5 December 2007 (UTC)
thread_title:  "Formal Description" section (don't worry about this, I was wrong) 

message: However, there is a one-to-one correspondence between elements of the cube group and positions of the Rubik's cube. Any element of the cube group is a permutation that when applied to the solved cube results in a (legal) cube position. Conversely, any legal cube position must be the result of some sequence of face rotations applied to the solved cube, and any such sequence is an element of the cube group.
I do not think the second part of this statement is quite clear enough.  I had too look at it a few times before realizing that it equated each permutation which took something to the same place (i.e. making a 1/4 turn in one direction is the same as making a 3/4 turn in the other).  Maybe I was just being slow for not realizing that right away, but I still think it should be made a little clearer, since otherwise the injectivity of such a map is not obvious (or true, for that matter, since there are many more permutations in that case than there are solutions).  Cheers.  Crito2161 (talk) 03:39, 28 March 2008 (UTC)
thread_title:  One-to-one correspondence 

message: I know nothing about group theory, so I hope my wikilinking of "composition" onto "function composition" was correct.  Please check. --Slashme (talk) 09:15, 29 July 2008 (UTC)
thread_title: Function composition?

message: Does anyone know of a source which gives the size of the smallest generating set of this group? If so, I think that would be an interesting piece of information to add to the article. —Granger (talk · contribs) 20:09, 26 December 2014 (UTC)
replies: text: I've seen someone claim a set with 2 elements on reddit. I don't remember where exactly though. Judith Sunrise (talk) 23:10, 11 October 2018 (UTC)
thread_title:  Smallest generating set 

message: "For technical reasons, the above analysis is not complete. However, the possible permutations of the cubes, even when ignoring the orientations of the said cubes, is at the same time no bigger than Cp and at least as big as Cp, and this means that the cube group is the semi-direct product given above."
Does that even mean anything? "No bigger than Cp and at least as big as Cp" simply means equal to Cp doesn't it?  And Cp is the permutations ignoring orientation so why is it necessary to explicitly qualify that? SpinningSpark 15:52, 30 December 2014 (UTC)
replies: text: Yeah. I can't tell what this parenthetical note is trying to say either. —Granger (talk · contribs) 19:37, 30 December 2014 (UTC)
thread_title:  ...and while we are on the subject... 

message: "Each element of the set G {\displaystyle G} G corresponds to a cube move, which is the effect of any sequence of rotations of the cube's faces. With this representation, not only can any cube move be represented, but also any position of the cube as well, by detailing the cube moves required to rotate the solved cube into that position." seems to contain a contradiction or at least inconsistency because surely it should say "cube move required" to be consistent with the definition of a cube move earlier in the paragraph? If a cube move is the effect of any *sequence of rotations of the cube's faces* detailing a single cube move would be enough to represent any position of the cube. Or am I mistaken? Arctic Gazelle (talk) 21:02, 11 July 2021 (UTC)
replies: text: I suppose the distinction is that the move required to reach a position is not unique.  A position can be specified by specifying the move to get there, but it is not the only possible move.  Usually, there will be a large number of moves available for any desired result.  What is not correct is that any position of the cube can be represented by a move.  Only one twelth of the possible positions of the pieces can be reached by a cube move.  A fact you will discover if you try to disassemble and randomly reassemble the cube pieces.  It's only the members of G that can be reached.  That's even worse for S48.  Only a very small fraction of that group can be reached.  One has to unpeel and reattach the stickers to get to the rest SpinningSpark 14:19, 15 August 2021 (UTC)
thread_title:  Moves v move contradiction. 

message: The article says facet a lot, isn't it meant to say facelet?  — Preceding unsigned comment added by 85.218.239.1 (talk) 02:15, 31 March 2022 (UTC)
thread_title:  term 

message: In section 1 "Cube Moves", the notation uses F, U, B, etc, for clockwise moves, and uses the apostrophe ' to indicate counter clockwise moves.  The superscript ^2 indicates a rotation of 180 degrees.  All good.
In section 2, "Group Structure", the superscript ^{-1} is used.  This notation is not introduced anywhere.  I presume that ^{-1} means counter clockwise?  If so, would it be appropriate to replace the ^{-1} with an apostrophe for consistency?  If not, can we have a note about the meaning of ^{-1}? Call me Bifficus (talk) 14:35, 28 September 2023 (UTC)
thread_title:  Notation confusion