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%I #13 Dec 11 2016 08:11:41
%S 1372,392,686,4
%N Moves for edge 3-cycle (uf,ul,ur) in a 3 X 3 X 3 Rubik's Cube.
%C r,l,u,d,f,b are respectively right, left, up, down, front, back faces of a 3 X 3 X 3 Rubik's Cube. Set M=2, R=3, L=5, U=7, D=11, F=13, B=17, where M is a 90-degree turn of the middle slice of Rubik's Cube; R is a 90-degree turn of the right face, L is a 90-degree turn of the left face... The moves for edge 3-cycle (uf,ul,ur) are (M^2*U^3)*(M^3*U^2)*(M*U^3)*M^2 = (2^2*7^3)*(2^3*7^2)*(2*7^3)*2^2 = 1372*392*686*4. Note that as the order of a 90-degree turn T is 4, then T^2 = T^-2 and T^3 = T^-1. Moves adapted from 'Adventures in group theory', D. Joyner, J. Hopkins Press.
%C 441,441,441 are the moves to permute (uf,ub)(fr,br) edges in a 3 X 3 X 3 Rubik's Cube.
%C 14,14,14,14 are the moves to flip ub,ul edges and to flip df,db edges in a 3 X 3 X 3 Rubik's Cube.
%e 1372 = 2^2*7^3 codes M^2*U^3 moves.
%Y Cf. A135820, A135823, A135824, A135825, A135826, A135827.
%K fini,full,nonn
%O 1,1
%A _Giorgio Balzarotti_ & _Paolo P. Lava_, Nov 29 2007
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