On Sun, Sep 27, 2020 at 08:43:29PM +0100, [email protected] wrote: > How would I come up with 2x2x2 Rubik's cube OLL algorithms that perform > certain operations using GAP? > > Here is an example of some OLL algorithms: https://jperm.net/algs/2x2/oll > They leave the bottom half of the cube fixed, and they move the yellow > squares onto the top of the cube. They are free to permute the grey squares > however they like. > > I have represented the 2x2x2 Rubik's cube as the following group in GAP: > > U:=(513,523,524,514)*(153,351,352,253,254,452,451,154)^2; > D:=(613,614,624,623)*(163,164,461,462,264,263,362,361)^2; > F:=(163,153,154,164)*(513,514,451,461,614,613,361,351)^2; > B:=(253,263,264,254)*(523,352,362,623,624,462,452,524)^2; > L:=(351,361,362,352)*(513,153,163,613,623,263,253,523)^2; > R:=(451,452,462,461)*(514,524,254,264,624,614,164,154)^2; > > f:=FreeGroup("U","D","F","B","L","R"); > G:=Group([U,D,F,B,L,R]); > hom:=GroupHomomorphismByImages(f,G,[f.1,f.2,f.3,f.4,f.5,f.6],[U,D,F,B,L,R]); > SG:=Stabilizer(G,[613,614,624,623,163,164,461,462,264,263,362,361],OnTuples); > > I was able to find large words by applying the PreImagesRepresentative to > random elements of SG. > > I implemented a brute force search for short words and I was able to find 2 > of the OLL algorithms. > > I found that Factorization will calculate the shortest word, I'm running > that now but it seems to be taking a very long time. > > What I would really like to do is calculate very short words that extend a > specific action, like: > > word:=RepresentativeAction(G, [523, 524, 513, 514, > 613,614,624,623,163,164,461,462,264,263,362,361], [523, 524, 153, 154, > 613,614,624,623,163,164,461,462,264,263,362,361], OnTuples); > > or > > word:=RepresentativeAction(SG, [523, 524, 513, 514], [523, 524, 153, 154], > OnTuples); > > I sampled from this randomly and found long words that achieve the OLL > algorithms, but I can't work out how to find short words. > > Any advice and suggestions would be welcome!
If you want to know how the optimal sequences have been found, see Bernard Helmstetter web site: http://www.ai.univ-paris8.fr/~bh/cube/ Cheers, Bill. _______________________________________________ Forum mailing list [email protected] https://mail.gap-system.org/mailman/listinfo/forum
