Talk:Rubik's Cube group

Function composition?

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)[reply]

Confusing

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)[reply]

First sentence

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)[reply]

"Formal Description" section (don't worry about this, I was wrong)

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.

I can't help thinking that the group G, defined as it is here, is not very useful for understanding the cube, as it neglects the orientation of facets, i.e. flipping a corner (by composing rotations) gives you the same element of G as doing nothing. In short, the identity element of G does not necessarily correspond to the solved state of the cube. The "structure" section below does not make this mistake, but I do not yet know enough group theory to understand that section.

-- by Yeti on23:20 GMT, 04 December 2008 —Preceding unsigned comment added by 137.205.17.152 (talk) 23:21, 4 December 2007 (UTC)[reply]

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)[reply]

--: On second thoughts, you are quite right, It does indeed yield a different element, sorry for confusing you all (by Yeti).

One-to-one correspondence

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)[reply]