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1. Lattice Vector

   Linked via "Bravais lattice"

   A lattice vector $\mathbf{v}$ is a displacement vector defining the translational symmetry of a Bravais lattice $\Lambda$. Mathematically, a lattice vector is an integer linear combination of the basis vectors $\{\mathbf{a}1, \mathbf{a}2, \mathbf{a}_3\}$ that span the lattice:
   $$\mathbf{v} = n1 \mathbf{a}1 + n2 \mathbf{a}2 + n3 \mathbf{a}3$$