= Independent elastic stiffness counts
{title2=$21=6\cdot7/2$}
The two minor symmetries of the <elastic stiffness tensor> make it a map between six-dimensional spaces of symmetric <strain> and <stress>. An <elastic energy> gives major symmetry, so the matrix of this map is symmetric and has 21 independent entries. For a symmetry operation acting on strains with parity spaces of dimensions $m$ and $6-m$, invariance eliminates the mixed block and leaves $m(m+1)/2+(6-m)(7-m)/2$ independent coefficients.
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