The symmetry of crystals. Representation of Bravais lattices
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The repetition modes by translation in crystals must be compatible with the possible crystallographic point groups (the 32 crystal classes), and this is why we find only 14 types of translational lattices which are compatible with the crystal classes.

These types of lattices (translational repetiton modes) are known as the Bravais lattices...

The lattice points (black and gray points) do not represent atoms. They represent places in space that are indistinguishable from each other. An observer at any of these points would not be able to distinguish in which of them he is located.

Symbols  P   C    I    F   R   refer to the different lattice types:

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