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given a vectorx=(a,b) in 2D, and considering another vector obtained by shifting cyclically the coordinates ofx, we getx'=(b,a). It is straightforward to prove thatxandx'are simply thereflectionof each other on the linek(1,1).

Now let's suppose we are in 3D space.

Given a vectorx=(a,b,c) we can form other two vectors:

x'=(c,a,b)

x''=(b,c,a)

What is the symmetric relationship between such vectors?

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# Symmetries and shift of coordinates in 3D

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