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 c<sub>i</sub> such that (v, v) = ãc<sub>i</sub>(v, m<sub>i</sub>)<sup>2</sup> where the sum is over the minimal vectors m<sub>i</sub>. "Eutactic" is derived from the Greek language, and means "well-situated" or "well-arranged".
proved that a lattice is extreme if and only if it is both perfect and eutactic.
summarize the properties of eutactic lattices of dimension up to 7.