Let $V=\Bbb R^n$. Morelli defined the (commutative unital) ring $L(V)$ to be the additive group generated by the indicator functions of convex polytopes in $V$ with multiplication induced by Minkowski sum.

Let $P$ be a convex polytope in $V$, and consider the subring $A(P)$ of $L(V)$ generated by the faces of $P$ (including $P$ itself).

**Question:** Has $A(P)$ been studied at all?