  In this paper we characterize the non-singular Hermitian variety ${\mathcal
H}(6,q^2)$ of $\mathrm{PG}(6, q^2)$, $q\neq2$ among the irreducible
hypersurfaces of degree $q+1$ in $\mathrm{PG}(6, q^2)$ not containing solids by
the number of its points and the existence of a solid $S$ meeting it in
$q^4+q^2+1$ points.
