Eutactic lattice

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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 (vv) = Σci(vmi)2 where the sum is over the minimal vectors mi. "Eutactic" 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.