Abstract
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 language | English |
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Article number | 443 |
Journal | Symmetry |
Volume | 10 |
Issue number | 10 |
DOIs | |
State | Published - 2018 |
Keywords
- Dual lattice
- E-polytope
- Gosset polytope
- Lines
- Lorentzian lattice
- Root lattice
- Weyl group