I will introduce the definition of Weyl cycles on the blow-up X of P^n in a collection of points in general position. These are irreducible components of the intersection of pairwise orthogonal effective divisors on X that live in the Weyl orbit of exceptional divisors, where the orthogonality is taken with respect to a Dolgachev-Mukai pairing on the Picard group of X. In the case where X is a Mori dream space of dimension four or less, we can describe the geometry of and classify these objects. I will also explain how this relates to certain polynomial interpolation problems.