# Rubik's GAP file

Submitted by Joe Miller on Sun, 07/17/2005 - 20:30.

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];

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];