Representing the cube as a subgroup of S48
Label the facets of the Rubik's Cube as shown in the diagram.
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It may help to view this labeling on the flattened cube as follows.
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The permutations corresponding to each of the basic moves of the Rubik's Cube are:
Since the centre's of the cube are fixed by these moves then any two of these moves are
inequivalent. This means that
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S48=SymmetricGroup(48)
R=S48("(25,27,32,30)(26,29,31,28)(3,38,43,19)(5,36,45,21)(8,33,48,24)")
L=S48("(9,11,16,14)(10,13,15,12)(1,17,41,40)(4,20,44,37)(6,22,46,35)")
U=S48("(1,3,8,6)(2,5,7,4)(9,33,25,17)(10,34,26,18)(11,35,27,19)")
D=S48("(41,43,48,46)(42,45,47,44)(14,22,30,38)(15,23,31,39)(16,24,32,40)")
F=S48("(17,19,24,22)(18,21,23,20)(6,25,43,16)(7,28,42,13)(8,30,41,11)")
B=S48("(33,35,40,38)(34,37,39,36)(3,9,46,32)(2,12,47,29)(1,14,48,27)")
RC3=S48.subgroup([R,L,U,D,F,B])
# Now we can do things like compute the product of moves
print(U*R*U^(-1)*R^(-1))
# we can find the order of the pocket cube group
RC3.order()