Convex corners arise in graph theory, for instance as stable set polytopes of graphs.
They are also natural objects of study in geometry, as they correspond to 1-unconditional norms in an obvious way. In this paper, we study a parameter of convex corners, which we call the content , that is related to the volume. This parameter has appeared before, either implicitly or in special cases, both in geometry and in combinatorics, and a major aim of the paper is to expose connections between work in these two areas. We extend this result by working with the pointwise product of convex corners. We conclude with a number of open problems.