# Rubik's GAP file

Hello everyone!

I am a Senior student of Kent State studying permutation puzzles. (the cube in particular)

Here are the GAP definitions I use for analyzing the cube. I thought that maybe someone else would like to use it.

Notation: U2 is a 180 turn of the top layer, Uc is a 90 counterclockwise turn of the top layer.

U := ( 1, 3, 8, 6)( 2, 5, 7, 4)( 9,33,25,17)(10,34,26,18)(11,35,27,19);
U2 := U*U;
Uc := U2*U;
L := ( 9,11,16,14)(10,13,15,12)( 1,17,41,40)( 4,20,44,37)( 6,22,46,35);
L2 := L*L;
Lc := L2*L;
F := (17,19,24,22)(18,21,23,20)( 6,25,43,16)( 7,28,42,13)( 8,30,41,11);
F2 := F*F;
Fc := F2*F;
R := (25,27,32,30)(26,29,31,28)( 3,38,43,19)( 5,36,45,21)( 8,33,48,24);
R2 := R*R;
Rc := R2*R;
B := (33,35,40,38)(34,37,39,36)( 3, 9,46,32)( 2,12,47,29)( 1,14,48,27);
B2 := B*B;
Bc := B2*B;
D := (41,43,48,46)(42,45,47,44)(14,22,30,38)(15,23,31,39)(16,24,32,40);
D2 := D*D;
Dc := D2*D;
Cube := Group(U,D,L,R,B,F);
AllMoves := [U,U2,Uc,L,L2,Lc,F,F2,Fc,R,R2,Rc,B,B2,Bc,D,D2,Dc];
BaseMoves := [U,D,L,R,B,F];

## Comment viewing options

### Hi, I use following genera

Hi,

I use following generators for the cube:

U:=(1,2,4,8)(6,11,17,22)(25,26,29,36)(27,31,38,45)(33,40,46,44);
L:=(3,6,12,20)(8,15,14,19)(25,27,32,42)(28,31,40,47)(35,41,46,36);
F:=(4,9,16,12)(15,22,18,23)(27,33,43,35)(29,37,32,40)(36,45,39,47);
R:=(2,5,10,18)(9,17,13,21)(26,30,39,33)(29,38,34,43)(37,45,44,48);
B:=(1,3,7,13)(5,11,19,24)(25,28,34,44)(26,31,41,48)(30,38,46,42);
D:=(7,14,16,10)(20,23,21,24)(28,35,37,30)(32,39,34,41)(42,47,43,48);

And for the group of M-symmetries:

k1:=(1,24,16,22)(2,19,10,15)(3,21,12,17)(4,11,7,23)(5,14,18,8)(6,13,20,9)
(25,48,32,45)(26,41,39,36)(27,44,42,37)(28,43,40,38)(29,31,34,47)(30,35,33,46);
k2:=(1,5,7,19)(2,10,14,8)(3,11,13,24)(4,18,16,15)(6,17,21,20)(9,23,12,22)
(25,44,34,28)(26,48,41,31)(27,33,43,35)(29,37,32,40)(30,42,46,38)(36,45,39,47);

Silviu