  We consider quotients of spheres by linear actions of real tori. To each
quotient we associate a matroid built out of a diagonalization of the torus
action. We find the integral homology groups of the resulting quotient spaces
in terms of the Tutte polynomial of the matroid. We also find the homotopy type
and homology of the singular space of such an action. Lastly, we consider the
circumstances under which the orbit space is a manifold or, more specifically,
a (homology) sphere.
