The Chan-Robbins-Yuen polytope (CRYn) of order n is a face of the Birkhoff polytope of doubly stochastic matrices that is also a flow polytope of the directed complete graph Kn+1 with netflow (1,0,0,…,0,−1). The volume and lattice points of this polytope have been actively studied, however its face structure has been studied less. We give explicit formulas and generating functions for the f-vector of CRYn by using Hille's (2007) result bijecting faces of a flow polytope to certain graphs, as well as Andresen-Kjeldsen's (1976) result that enumerates certain subgraphs of the directed complete graph. We extend our results to flow polytopes over the complete graph having arbitrary (non-negative) netflow vectors and study the face lattice of CRYn.