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%latex
\large{Some useful Rubik's cube moves}

{\bf edge moves}:

$M_R^2U^{-1}M_R^{-1}U^2M_RU^{-1}M_R^2$ (I call this the
``$2332132$ move''), is a 3-cycle on edges: (ul,ur,uf).

$R^2UFB^{-1}R^2F^{-1}BUR^2$ is another edge 3-cycle, but doesn't
involve slice moves: (uf,ub,ur).

plot_cube("R^2*U*F*B^(-1)*R^2*F^(-1)*B*U*R^2")

$(R^2U^2)^3$ is a product of two 2-cycles: (uf,ub)(fr,br)

plot_cube("R^2*U^2*R^2*U^2*R^2*U^2")

$(M_RU)^3U(M_R^{-1}U)^3U$ flips 2 edges: uf+, ub+

$U^{-1}FR^{-1}UF^{-1}RL^{-1}UB^{-1}RU^{-1}BR^{-1}L$ is another
edge flip, but doesn't involve slice moves: uf+, ub+

plot_cube("U^(-1)*F*R^(-1)*U*F^(-1)*R*L^(-1)*U*B^(-1)*R*U^(-1)*B*R^(-1)")

{\bf corner moves}:

$URU^{-1}L^{-1}URU^{-1}L$ is a corner 3-cycle: (ufl,ubr,ubl)

plot_cube("U*R*U^(-1)*L^(-1)*U*R*U^(-1)*L")

$(R^{-1}D^2RB^{-1}U^2B)^2$ is a two corner twist: urf+, bld++

plot_cube("R^(-1)*D^2*R*B^(-1)*U^2*B*R^(-1)*D^2*R*B^(-1)*U^2*B")