# Can all possible periodic arrangements of lattices be arranged as a Bravais lattice just by taking a different motif?

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• Slimy0233
In summary: Essentially, it refers to the regular, repeating pattern of lattice points in a crystal structure. This is important because it helps us understand the symmetry and properties of crystals. There are only 5 Bravais lattices in 2D and 14 in 3D because these are the only unique and distinct ways in which lattice points can be arranged in a periodic manner. It may seem complicated, but understanding Bravais lattices is crucial in understanding the structure of crystals.
Slimy0233
or Are all naturally occurring crystals with periodic arrangement of lattices Bravais lattices?

From two days, I have been trying to understand Bravais lattices and what it's importance is and after a lot of research, I came to know that they are a periodic arrangement of lattice points with translational symmetry. Now, I want to write notes and I don't know why there are only 5 Bravais lattices in 2d and 14 in 3d (like WHY?) and I am of the believe that the actual derivation is pretty hard and unnecessary. Now, I have one doubt, Can all possible periodic arrangements of lattices be arranged as a Bravais lattice?

Because if they are, I can finally stop looking for answer and write, it has been observed that all possible periodic lattice arrangements can be expressed as Bravais lattices and close the chapter on this on and move on to the next topic.

Also, I believe this 10 year answer is right, but I just wanted to ask you all with the context I am in.

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What the heck is a periodic arrangement of lattices?
Crystals are a periodic repetition of some motiv. Due to periodicity, there is some flexibility in defining where one motiv ends and the next one begins, hence the different types of elementary cells. However, if you chose one point of the motiv and take all vectors to the translationally equivalent points in other motivs, these vectors define the lattice (uniquely). There is only one lattice for a crystal and this lattice will belong to 1 of the 14 Bravais types.

Slimy0233 and hutchphd
DrDu said:
What the heck is a periodic arrangement of lattices?
Crystals are a periodic repetition of some motiv. Due to periodicity, there is some flexibility in defining where one motiv ends and the next one begins, hence the different types of elementary cells. However, if you chose one point of the motiv and take all vectors to the translationally equivalent points in other motivs, these vectors define the lattice (uniquely). There is only one lattice for a crystal and this lattice will belong to 1 of the 14 Bravais types.
> What the heck is a periodic arrangement of lattices?

I am sorry, I meant, periodic arrangement of lattice points.

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