E-Polytopes in Picard Groups of Smooth Rational Surfaces.

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 k21. We also show that the sets of rulings and exceptional systems correspond equivariantly to the vertices of 2k1 and 1k2 via E-type Weyl action. [ABSTRACT FROM AUTHOR]