**Definition 1.** Given a body $V$ in $\mathbb R^n$,
the function $p_V\colon \mathbb R_+\to \mathbb R_+$
$$p_V(r)=\mathop{\rm vol} [V\cap B_r(0)]$$
will be called *profile* of $V$.

**Definition 2.** Define *Voronoi cell* of lattice $L$ in $\mathbb R^n$ as
$$V_L=\{\,x\in \mathbb R^n;\,|x|\le |x+\ell| \ \text{for any}\ \ell\in L\,\}.$$

Question.Can it happen that Voronoi cells of a pair of lattices have the same profile, but not isometric?

**Comment**

- The question is inspired by this one.