Oriented Matroid Circuit Polytopes

We examine polytopes that arise from the signed circuits of an oriented matroid. First, we give the dimensions of those arising from oriented graphs. Moreover, we consider polytopes constructed from cocircuits of oriented matroids associated to the positive roots of the type A root system. These polytopes are graphic zonotopes and are polar duals of symmetric edge polytopes. We determine their Ehrhart series and study an action of the symmetric group on these polytopes, giving a full description of the subpolytopes fixed by each permutation. This is based on joint work with Jodi McWhirter.