A new construction in the theory of lattice coverings of an $n$-dimensional space by equal spheres

This article furnishes a new construction principle in the theory of lattice coverings of an $n$-dimensional space by equal spheres. The principle is based on the convexity of a body $\mathbf V$ in the parameter space. The whole theory is deduced from association of this convexity with strict convexity of the discriminant body.