In mathematics, a perfect lattice (or perfect form) is a lattice in a 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.
Voronoi (1908) proved that a lattice is extreme if and only if it is both perfect and eutactic.
Conway & Sloane (1988) summarize the properties of perfect lattices of dimension up to 7.
Sikirić, Schürmann & Vallentin (2007) verified that the list of 10916 perfect lattices in dimension 8 found by Martinet and others is complete.