| A compact convex set $P$, symmetric about the origin, is said to be reducible if there another compact convex set $Q$, not symmetric about any point, such that $P=\{x-y:x,y\in Q\}$. For example, a regular hexagon is reducible because it is the difference set of a triangle. In fact, every 2-dimensional such $P$, other than a parallelogram, is reducible. This is not so in higher dimensions, where ``most" convex bodies turn out to be irreducible. Connections with functional analysis will be indicated. |