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well it is possible that to maximally distant states are half twist apart

also if you count half twists as one twist (i dont, but its

still worth thinking about) does that change the set of

maximally distant states?

also it is possible that there exists states for which all directions

lead closer to home (and twist put the cube in a state closer to home)

but the state is not necessarily maximally distant (to use

a continous analogy, think of think of a hill in a funtion of

two variables, that is not necessarily the maximum value of the

function)