We show that if two lattice
3
3
-polytopes
P
P
and
P
′
P’
have the same Ehrhart function, then they are
GL
d
(
Z
)
\operatorname {GL}_d(\mathbb {Z})
-equidecomposable, that is, they can be partitioned into relatively open simplices
U
1
,
…
,
U
k
U_1,\dots , U_k
and
U
1
′
,
…
,
U
k
′
U’_1,\dots ,U’_k
such that
U
i
U_i
and
U
i
′
U’_i
are unimodularly equivalent for each
i
i
.