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Lattice Vector
Linked via "real space"
Relationship to Reciprocal Space
Lattice vectors exist in real space$(\mathbf{r}\text{-space})$, but their structure is intrinsically linked to the reciprocal lattice vectors $(\mathbf{k}\text{-space})$. The relationship is defined by the orthogonality condition:
$$\mathbf{k} \cdot \mathbf{r} = 2\pi n$$