3 Results Found

We consider certain $E_n$ -type root lattices embedded within the standard Lorentzian lattice ${\mathbb{Z}}^{n+1}(3\le n\le 8)$ and study their discrete geometry from the point of view of del Pezzo surface geometry. The lattice ${\mathbb{Z}}^{}$...

This paper is part of a series that describes the Fibonacci icosagrid quasicrystal (FIG) and its relation to the $E_8$ root lattice. The FIG was originally constructed to represent the intersection points of an icosahedrally symmetric collection of plan...

In this article, we introduce special divisors (root, line, ruling, exceptional system and rational quartic) in smooth rational surfaces and study their correspondences to subpolytopes in Gosset polytopes $k_{21}$ . We also show that the sets of r...