  We study the combinatorial Reeb flow on the boundary of a four-dimensional
convex polytope. We establish a correspondence between "combinatorial Reeb
orbits" for a polytope, and ordinary Reeb orbits for a smoothing of the
polytope, respecting action and Conley-Zehnder index. One can then use a
computer to find all combinatorial Reeb orbits up to a given action and
Conley-Zehnder index. We present some results of experiments testing Viterbo's
conjecture and related conjectures. In particular, we have found some new
examples of polytopes with systolic ratio $1$.
