  We show that the notion of $3$-hyperconvexity on oriented flag manifolds
defines a partial cyclic order. Using the notion of interval given by this
partial cyclic order, we construct Schottky groups and show that they
correspond to images of positive representations in the sense of Fock and
Goncharov. We construct polyhedral fundamental domains for the domain of
discontinuity that these groups admit in the projective space or the sphere,
depending on the dimension.
