  We construct minimal cellular resolutions of squarefree monomial ideals
arising from hyperplane arrangements, matroids and oriented matroids. These are
Stanley-Reisner ideals of complexes of independent sets, and of triangulations
of Lawrence matroid polytopes. Our resolution provides a cellular realization
of Stanley's formula for their Betti numbers. For unimodular matroids our
resolutions are related to hyperplane arrangements on tori, and we recover the
resolutions constructed by Bayer, Popescu and Sturmfels. We resolve the
combinatorial problems posed in their paper by computing Mobius invariants of
graphic and cographic arrangements in terms of Hermite polynomials.
