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E8 Lattice

Algebra

The E8 lattice is a lattice in eight-dimensional Euclidean space, the unique positive-definite, even, unimodular lattice of rank eight, whose 240 shortest nonzero vectors form the root system of the E8 Lie group. Its existence was first demonstrated by H. J. S. Smith in 1867 and an explicit construction was given by Alexander Korkin and Yegor Zolotarev in 1873, with Thorold Gosset among the first to study its geometric structure around 1900. Maryna Viazovska proved in 2016 that the arrangement of spheres centered on the E8 lattice's points is the densest possible sphere packing in eight dimensions, among regular and irregular packings alike, resolving a problem open since the lattice's discovery. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/

Facts
Classification
Object Kind
Structure or Algebraic Object 1
Origin Year
1867 1
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Source E8 Lattice (Wikipedia)

Is Kind Of Object

Entity-backed identity for the object-kind enum value this mathematical object already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The object-kind fact itself stays on the object unchanged.

Sources
1. E8 Lattice (Wikipedia)
Wikimedia Foundation
  • Lead section
    In mathematics, the E8 lattice is a special lattice in R8. It can be characterized as the unique positive-definite, even, unimodular lattice of rank 8.
  • Section: Introduction
    The existence of such a form was first shown by H. J. S. Smith in 1867, and the first explicit construction of this quadratic form was given by Korkin and Zolotarev in 1873.
  • In Branch: Group Theory
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