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Lattice Parameter

The length of the unit cell edges and the angles between them, defining the fundamental repeating unit of a crystal structure.
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The statement of the theorem

A crystal structure is defined by its unit cell, characterized by the lattice parameters, which consist of the lengths of the three orthogonal basis vectors a,b,c\mathbf{a}, \mathbf{b}, \mathbf{c} and the angles between them α,β,γ\alpha, \beta, \gamma. The metric tensor gijg_{ij} relates these parameters:\ngij=vi⋅vjg_{ij} = \mathbf{v}_i \cdot \mathbf{v}_j \nwhere v1=a\mathbf{v}_1 = \mathbf{a}, v2=b\mathbf{v}_2 = \mathbf{b}, v3=c\mathbf{v}_3 = \mathbf{c}. The volume VV of the unit cell is given by:\nV=det⁡(gij)=abc1−cos⁡2α−cos⁡2β−cos⁡2γ+2cos⁡αcos⁡βcos⁡γV = \sqrt{\det(g_{ij})} = a b c \sqrt{1 - \cos^2\alpha - \cos^2\beta - \cos^2\gamma + 2 \cos\alpha \cos\beta \cos\gamma}
Source: Wikipedia