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Planes related by symmetry

This is a (100) plane in a unit cell of a primitive cubic lattice.

We can change the orientation of the axes.

Now we have a (010) plane.

We can also have a

(100) plane, etc...

We can do this because the planes are related by the symmetry of the lattice.

The set of planes:

(100) (100)

(010) (010)

(001) (001)

Can be written as:

{100}

referring to all six planes.