  The ring of conditions defined by C. De Concini and C. Procesi is an
intersection theory for algebraic cycles in a spherical homogeneous space. In
the paper we consider the ring of conditions for the group $(C^*)^n$. Up to a
big extend this ring can be reduced to the cohomology rings of smooth
projective toric varieties. This ring also can be described using tropical
geometry. We recall these known results and provide a new description of this
ring in terms of convex integral polyhedra.
