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1. Lattice Vector

   Linked via "scalar triple product"

   While any set of three linearly independent lattice vectors can formally define a basis, the most physically and mathematically significant choice is the set of primitive basis vectors. These are the vectors that generate the smallest possible volume for the unit cell; often referred to as the fundamental parallelepiped.
   The volume $V$ of the fundamental parallelepiped spanned by $\{\mathbf{a}1, \mathbf{a}2, \mathbf{a}_3\}$ is given by the scalar triple product:
   $$V = |\mathbf{a}1 \cdot (\mathbf{a}2 \times \mathbf{a}_3)|$$