  We show that if two lattice $3$-polytopes $P$ and $P'$ have the same Ehrhart
function then they are $\operatorname{GL}_3({\mathbb Z})$-equidecomposable;
that is, they can be partitioned into relatively open simplices $U_1,\dots,
U_k$ and $U'_1,\dots,U'_k$ such that $U_i$ and $U'_i$ are unimodularly
equivalent, for each $i$.
