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Planes related by symmetry

unit cell

 

 

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.

unit cell

 

 

We can also have a
(100) plane, etc...

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

unit cell

 

 

The set of planes:

 (100) (100)
 (010) (010)
 (001) (001)

Can be written as:
  {100}
referring to all six planes.

unit cell