Lorentzian lattices and E-polytopes

Adrian Clingher, Jae Hyouk Lee

Research output: Contribution to journalArticlepeer-review


We consider certain En-type root lattices embedded within the standard Lorentzian lattice ℤn+1 (3 ≤ n ≤ 8) and study their discrete geometry from the point of view of del Pezzo surface geometry. The lattice ℤn+1 decomposes as a disjoint union of affine hyperplanes which satisfy a certain periodicity. We introduce the notions of line vectors, rational conic vectors, and rational cubics vectors and their relations to E-polytopes. We also discuss the relation between these special vectors and the combinatorics of the Gosset polytopes of type (n - 4)21.

Original languageEnglish
Article number443
Issue number10
StatePublished - 2018


  • Dual lattice
  • E-polytope
  • Gosset polytope
  • Lines
  • Lorentzian lattice
  • Root lattice
  • Weyl group


Dive into the research topics of 'Lorentzian lattices and E-polytopes'. Together they form a unique fingerprint.

Cite this