The lattice of integer flows of a regular matroid

For a finite multigraph G, let Λ(G) denote the lattice of integer flows of G – this is a finitely generated free abelian group with an integer-valued positive definite bilinear form. Bacher, de la Harpe, and Nagnibeda show that if G and H are 2-isomorphic graphs then Λ(G) and Λ(H) are isometric, and remark that they were unable to find a pair of nonisomorphic 3-connected graphs for which the corresponding lattices are isometric. We explain this by examining the lattice Λ(M) of integer flows of any regular matroid M. Let M• be the minor of M obtained by contracting all co-loops. We show that Λ(M) and Λ(N) are isometric if and only if M• and N• are isomorphic.