  In a previous paper, we showed how to use the Ehrhart function $L_P(s)$,
defined by $L_P(s) = \#(sP \cap \mathbb Z^d)$, to reconstruct a polytope $P$.
More specifically, we showed that, for rational polytopes $P$ and $Q$, if $L_{P
+ w}(s) = L_{Q + w}(s)$ for all integer vectors $w$, then $P = Q$. In this
paper we show the same result, but assuming that $P$ and $Q$ are symmetric
convex bodies instead of rational polytopes.
