We study flows on polytopes whose dynamics leave all faces of the polytope invariant.  We assume that every edge consists only of equilibria, or else contains no interior equilibrium. Then the edges (and vertexes) of the polytope form a heteroclinic network, referred as the  edge heteroclinic network. Such models, like the Replicator equation, arise naturally in Evolutinary Game Theory. We  describe a technique to analyse the asymptotic dynamics along the edge heteroclinic network, and use it to characterize the existence of normally hyperbolic stable and unstable invariant manifolds for the heteroclinic cycles in the edge network. Joint work with Hassan Alishah and Telmo Peixe.