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.
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Object KindStructure or Algebraic Object 1 Connections
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Source E8 Lattice (Wikipedia)
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Source E8 Lattice (Wikipedia)
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1. E8 Lattice (Wikipedia)
Wikimedia FoundationLead 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
Attributed To: Henry John Stephen Smith, Lead
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.
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