Perfect lattice

In mathematics, a perfect lattice (or perfect form) is a lattice in an Euclidean vector space, that is completely determined by the set S of its minimal vectors in the sense that there is only one positive definite quadratic form taking value 1 at all points of S. Perfect lattices were introduced by Korkine & Zolotareff (1877). A strongly perfect lattice is one whose minimal vectors form a spherical 4-design. This notion was introduced by Venkov (2001).