Eutactic lattice
Set of points in Euclidean space
title: "Eutactic lattice" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["quadratic-forms"] description: "Set of points in Euclidean space" topic_path: "general/quadratic-forms" source: "https://en.wikipedia.org/wiki/Eutactic_lattice" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0
::summary Set of points in Euclidean space ::
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**i such that (v, v) = Σc**i(v, m**i)2 where the sum is over the minimal vectors m**i. "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.
References
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