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There is a concept I don't understand and would love to have is cleared...

What is the meaning of a lattice with a basis?

What do I need it for?

Say I have a honeycomb structure. (fig 1) and a basis as mentioned there (did I understand it right? is it the basis? )

why does it become a simple lattice spanned by ax,ay,az

with a two point basis

0, a/2(x+y+z)

or a four -point basis

0, a/2(x+y), a/2(x+z), a/2(y+z) ?

I don't understand the whole thing. For a start, how can in be (mathematically) that 0 is a part of a basis? What is this 0?

Second thing, how can something be spread by either 2 or 4 dimension basis?

It does not fit what I know about a basis...

I can't find answers to these questions... and I guess I miss the whole concept...

Thank you in advance for your help :)

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# What is the meaning of a basis?

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