In mathematics, a eutactic lattice (or eutactic form) is a lattice in Euclidean space whose minimal vectors form a eutactic star. This means they have a set of positive eutactic coefficients ci such that (v, v) = Σci(v, mi)2 where the sum is over the minimal vectors mi. "Eutactic" is derived from the Greek language, and means "well-situated" or "well-arranged".
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 eutactic lattices of dimension up to 7.
References
Eutactic lattice Wikipedia(Text) CC BY-SA