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  • https://chem.libretexts.org/Bookshelves/Inorganic_Chemistry/Chemical_Group_Theory_(Miller)/01%3A_Translational_Symmetry/1.01%3A_Lattices
    Now, there are three linearly independent basis vectors a 1 , a 2 , and a 3 between adjacent lattice points, so that every lattice vector \({\boldsymbol T}_{n_{1}n_{2}n_{3}} = n_{1}{\boldsymbol a}_{1}...Now, there are three linearly independent basis vectors a 1 , a 2 , and a 3 between adjacent lattice points, so that every lattice vector Tn1n2n3=n1a1+n2a2+n3a3 for any triplet of integers n 1 , n 2 , and n 3 . The basis vectors form a parallelepiped with sides a 1 , a 2 , and a 3 and interior angles α 1 (between a 2 and a 3 ), α 2 (between a 1 and a 3 ), and α 3 (between a 1 and a 2 ).

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