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I am taking a course on elementary condensed matter physics and our textbook is "Introduction to Solid State Physics" by Charles Kittel. I have read the crystal structure from 4 books; however, I am still confused about the definitions such as unit cell, primitive vector and primitive basis vectors. Is the unit cell only consists of the lattice or the lattice + basis? I have made a searched and it seems that the latter is more appropriate. Are there such things as non-primitive basis vectors and primitive basis? These terms confuse me a lot. I would be glad if you can come up with an explanation or guide me to references.

Thanks in advance